Poster Abstracts
1.Usefulness Of Approximate Entropy For Studying Heart Rate Variability In Chagas' And Arterial
Hypertension Diseases During Head-Up Postural Test
Luiz O. Murta Jr., Departamento de Física e Matemática - FFCLRP - USP, murta@ffclrp.usp.br
Katia C. Nakazato, Divisão de Cardiologia - FMRP - USP
Júlio C. Crescêncio, Divisão de Cardiologia - FMRP - USP
Renata T. Kozuki, Divisão de Cardiologia - FMRP - USP
Benedito C. Maciel, Divisão de Cardiologia - FMRP - USP
Lourenço Gallo Jr, Divisão de Cardiologia - FMRP - USP
Heart Rate Variability (HRV) is dependent on the modulation of two opposing efferent nerve drives acting on the heart:
one stimulatory (sympathetic) and another inhibitory (parasympathetic). The complex interaction of this modulation,
associated to its changes in response to different environmental stimuli, is responsible for nonlinear dynamics (NLD) in
HRV. Approximate entropy (AE) has shown a suitable method for measuring NLD of HRV. Aims: to quantify HRV using AE in
cardiac patients (with small cardiac damage) with different types of autonomic dysfunction, i.e., Chagas' disease and
essential hypertension. Methods: we compared AE and linear parameters (time and frequency domains) in collected R-R time
series (for 15 min) at rest condition, before and after the transition from horizontal to a vertical position (70 degrees)
during passive (custom made table) head-up tilt test. Groups studied: 13 normal subjects aged 38±9 years (mean ± standard
deviation), 21 patients with Chagas' disease aged 51±6 years and 22 with chronic hypertension aged 42±7 years. The patients
were studied in the absence of any medication.Results: no statistical differences in each position could be found in the
inter and intra group analysis. However, comparing HRV postural changes, by linear and nonlinear methods, only AE detected
a lower HRV response in the chagasic group. Conclusion: AE, compared to classical linear methods of HRV, has shown a higher
sensitivity for detecting mild degrees of neural dysfunction, as seen in chagasic patients included in the present study.
2.Investigating The Relationship Between System Complexity And Stability: Time Series Irregularity And Global Network
Connectance As Possible Indicators Of Physiological Flexibility In Plant Species
Daniel Santa Cruz Damineli, Masters program student in Plant Biology at Intituto de Biociências, UNESP, Campus Rio Claro,
SP & Laboratório de Ecofisiologia Vegetal UNOESTE, Presidente Prudente, SP, danieldamineli@gmail.com
Gustavo Maia Souza, Laboratório de Ecofisiologia Vegetal UNOESTE, Presidente Prudente, SP.
The main focus of our research project is to investigate the relationship between system complexity and stability. There
are several aspects that can be studied to address this matter, and on the current work we approach particularly time
series irregularity and network connectance. This has been carried out under a biological perspective, in the context of
functional groups of tropical forest succession. There are two main functional groups that characterize plant species in
the tropical forest succession: the pioneers, fast-growing light-demanding species, and the secondaries, slow-growing and
shade tolerant (Bazzaz and Pickett, 1980). The most accepted hypothesis concerning the physiological flexibility of these
groups is the multiple-resources model (Bazzaz and Pickett, 1980) which states that pioneers are more flexible due to the
multiple-resources variability present in their growth environments.
Organism metabolism, as well as environmental factors, display non-linear dynamics making the perspective of global stability
unlikely (Møller and Swaddle, 1997). Therefore in an oscillating environment, chaotic dynamics appear to be adaptive, since
they allow flexibility in response to perturbations (Souza and Oliveira 2004). According to Møller et al. (1998) this is due
to the property of chaotic attractors to coexist with several unstable periodic orbits in such a fashion that, when facing
perturbations, a given system may remain chaotic or establish its dynamics in the neighboring orbits. In addition, Peixoto’s
theorem demonstrated that chaotic dynamics are structurally more stable when perturbed (Fiedler-Ferrara and Prado 1994).
Interestingly, the observation of chaotic behavior in biological systems has been increasingly frequent (May, 1989,
Mosekild and Mosekild, 1991, Çambel, 1993) also in plant physiology studies (Lüttge and Beck, 1992; Shabala et al., 1997,
Souza et al., 2004).
In this study our hypothesis is that the differences in physiological flexibility attributed to the pioneers are related to
more complex dynamics together with a greater control of the underlying physiological processes. In order to evaluate such
hypothesis, time series of the gas exchange dynamics of a pioneer (Cecropia pachystachya Trec.) and a secondary (Tabebuia
alba (Cham.) Sandw.) species were analyzed using an algorithm named Approximate Entropy (ApEn), a measure of irregularity
(Pincus, 1991), and global network connectance (Cg), a measure of the strength of correlation among physiological variables
in a hypothetical physiological network. If the working hypothesis is correct, greater values of ApEn and Cg are expected
for the pioneer species.
To generate the gas exchange time series, an infra-red gas analyzer (IRGA) was used measuring gas exchange variables
(transpiration, E, CO2 assimilation, A, stomatal conductance, gs, and intercellular CO2 concentration, Ci) in a single
sapling leaf, in three individuals of each specie. Measures were taken at 10 seconds interval during 6 consecutive hours,
in constant environmental conditions at the sample chamber. On this particular study the environmental conditions were
maintained constant in order to assess the intrinsic dynamics of each species.
The computation of ApEn requires the specification of two input parameters, a run length m and a tolerance window r. The
resulting irregularity parameter measures the logarithmic likelihood that runs of patterns that are close (within r) for m
contiguous observations remain close (within the same tolerance width r) on next incremental comparisons. This analysis was
focused on gs dynamics since stomatal aperture is an essential factor both in regulation of transpiration and net
photosynthesis.
The network connectance analysis, being the strength of relationship between pairs of variables, was performed based on
Souza et al. 2004b. First, it is established linear correlations (r values) between pairs of gas exchange variables (gs-A,
gs-E, gs-Ci, A-E, A-Ci). Then the r values are z-transformed, z = 0.5 Ln [(1 + r)/(1 – r)], and the global network
connectance (Cg) is calculated as the mean of z values (Amzallag, 2001).
The measured values of the gas exchange variables were compatible with the expected difference between pioneer and
secondary species (Strauss-Debenedetti and Bazzaz, 1996, Souza et al., 2004c, Ribeiro et al., 2005). The pioneer species
displayed greater mean values (p<0.05) of A, E and gs.
The obtained ApEn values indicate that the pioneer species has a more irregular stomatal conductance (gs) dynamics
(ApEn = 2.017) compared to the secondary species (ApEn = 1.666). When comparing time series it can be observed that the
secondary species displayed a consistent oscillatory pattern (regular) whereas no regular pattern can be seen in the pioneer
species dynamics. These results are coherent with previous work, according to Souza and Oliveira (2004) e Souza and
Buckeridge (2004), biological systems with more complex dynamics would have greater ability to respond to environmental
changes, optimizing its homeostatic capacity. In other words, more complex dynamics would confer greater flexibility,
therefore, greater adaptability to biological systems immerse into a changing environment. In an experiment with plants
under water deficit Souza et al. (2004a) observed that plants with a more irregular stomatal aperture (gs) dynamics
displayed a greater ability restoring gas exchange values close to values before the perturbation. The same relationship
was observed among bean genotypes with different water deficit tolerance, where the genotype with greater homeostatic
ability displayed a greater complexity on its gas exchange dynamics (Souza et al., 2005). Global network connectance values
were also coherent with this perspective since the pioneer specie showed Cg value of 1.287 and the secondary of 0.702.
The results presented in this study suggest the greater flexibility in response to environmental changes attributed to the
pioneer species could be conferred by more complex physiological dynamics and a more connected physiological network.
However, in order to have a consistent corroboration of the hypothesis, studies with a larger number of species and dealing
with responses to perturbations are needed. Also, it is important to use a more comprehensive tool-kit to test time-series
complexity, since irregularity is not the only approach to complexity (Goldberger et al., 2002). Finally, the network
connectance analysis could be improved by the use of algorithms that considers both linear and non-linear relationships to
establish correlations among variables, such as mutual information (Celluci et al., 2005).
3.Regular Chaotic And Deterministic Regimes In Human Mind
Kolombet Valeriy, Institute of Theoretocal and Experimental Biophysics of Russian Acad. Sci., kolombet@iteb.ru
Intellectual Reaction of Human Mind on External Signal (IRHMES) has firstly described in [1,2]. IRHMES represents as a rule
8 stages of the same mental volume corresponding to input of information (1 stage), to 6 stages of the information
processing (that looks like subsequent comparison of the input data with positive and negative data stored in memory) and to
forming the decision (1 stage). In case of stress the 8-step “mental trace” goes vice versa: immediate reaction and then
mental work to process input data.
Fine structure of IRHMES stages has described in [3]. As a rule each stage consists of 4 sub-stages. Well known particular
consequence of the fine structure existence is domination of 4-lines structure of poems.
There are 2 main methods for IRHMES investigation: verbal tracing of examinee and analysis of structure of literary works –
novels, poems, political tractates, fundamental religious books, etc. IRHMES in easy seen for trained expert; reproductively
of results is guaranteed by repetition of the verbal tracing and by checking of other literary works of the same author.
Mental health and set of mental abnormalities are recognizable in IRHMES. Stages 3 and 6 correspond to scan of areas of the
most emotional memory. Here additional fine structures are recognized that represent zones of chaotic thinking and between
them also zones of Alternative Self-Recognitions (ASRs). Qualitative model of the situation is as followed. Normal case has
no ASRs; Usual way of Self-Recognition (USR) in course if its interaction with the most emotional areas of memory is stable.
More complex situation is in case when the interaction has broken. No-self-recognition and also associations with chaotic
phenomena are found in this situation. Next stage of complicity corresponds to appearance of the island of ASR in middle of
area of the chaotic thinking. Then (with growth of emotions) island of new chaotic thinking appears in centre of the first
ASR, etc. This way a symmetrical hierarchy of more and more emotional/devine ASRs appears in stages 3 and 6 of IRHMES. The
experimental results look like development of set of bifurcations in state of human thinking conduction growth of emotional
level.
There is wide spectrum of consequences of ASRs existence. In particular the mental traces are distorted in these regions
that essentially affects quality of thoughts.
Reference:
1. V. Kolombet. Mental worlds. Consciousness and physical reality. 1997. v. 2 , iss. 4, pp. 15-24 .
2. V. Kolombet. Transphysical worlds. In: V. Kolombet. Transphysical worlds. Origin of names. Moscow: Kron-Press, 2001, 864 p.
3. V. Kolombet. “Stendal syndrome” in light of hypnography. Practical psychology and psychoanalysis. 2003. v. 2 , pp. 11-27.
4.Oscillatory Dynamics During The Electrooxidation Of Methanol On Platinum And Tin-Platinum Surfaces
Silvia Helena Bonilla, Laboratório de Fisicoquímica Teórica e Aplicada, LaFTA, Instituto de Ciências Exatas e Tecnología,
Universidade Paulista, shbonilla@hotmail.com;bonilla@unip.br
Javier Rodríguez, Laboratorio de Electroquímica Fundamental, Facultad de Ciencias, Universidad de la República, Iguá 4225,
CP 11400, Montevideo, Uruguay.
C. Fernando Zinola, Laboratorio de Electroquímica Fundamental, Facultad de Ciencias, Universidad de la República, Iguá 4225,
CP 11400, Montevideo, Uruguay.
Cecilia M. V. B. Almeida, Laboratório de Fisicoquímica Teórica e Aplicada, LAFTA, Instituto de Ciências Exatas e Tecnología,
Universidade Paulista, Dr. Bacelar 1212, CEP 04026 002 São Paulo, Brazil.
Biagio F. Giannetti, Laboratório de Fisicoquímica Teórica e Aplicada, LAFTA, Instituto de Ciências Exatas e Tecnología,
Universidade Paulista, Dr. Bacelar 1212, CEP 04026 002 São Paulo, Brazil.
The investigation of methanol oxidation on a Pt electrode has attracted attention considering its application on direct
methanol fuel cells. It is well known that the addition of Sn improves the catalytic activity of Pt towards methanol
electro-oxidation as alloys. In the present work, Sn spontaneous deposition was conducted by immersion of polycrystalline
(pc) Pt into an aged 10-4 M SnSO4 +1 M H2SO4 solution for 5 min. The process occurs via self transformation of Sn(II) into
Snad on Pt and Sn4+ soluble species.
Although the presence of bistability and oscillations during methanol oxidation is already discussed in the current
literature, no relative information is available regarding methanol oxidation onto Sn-Pt.
In the present work, electrochemical impedance spectroscopy is used as a predictive tool to evaluate the stability of the
systems, as earlier proposed by Koper [1]. In this way, both Pt/Methanol and Sn-Pt/methanol systems exhibited negative
impedance in the Nyquist diagram under specific experimental conditions. These systems, presenting a negative real part for
a range of non-zero frequencies but with a positive zero-frequency impedance value, are expected to oscillate under
galvanostatic conditions [1]. Galvanostatic transients recorded on both surfaces exhibit different oscillatory patterns,
probably related to alternative methanol oxidation pathways at potentials (ca. 0.7 V) where water discharge takes place on
Pt and Sn-Pt electrodes. At this potential value, the formation of Pt(OH)ad or Sn(OH)+ad species is voltammetrically
observed, which are responsible of methanol adsorbate oxidation (Langmuir-Hinshelwood mechanism).
[1] M. T. M. Koper, J. Electroanal. Chem. 409 (1996) 175.
5.Control Of The Intensity Of A Wave Interacting With Charged Particles
De Ninno Giovanni, Sincrotrone Trieste, giovanni.deninno@elettra.trieste.it
The interaction between a wave and a bunch of charged particles is encountered in many branches of applied physics ranging
from particle accelerators to laser physics (Free Electron Laser). Generically, this self-consistent interaction leads to
an exponential increase of the intensity of the wave due to the formation of clusters of charged particles. However, after a
transient time, these clusters lead to undesirable oscillations of the intensity of the wave. There is therefore a crucial
need to control the dynamics of these systems in order to improve the performance of the devices.
The wave-particle interaction can be cast in a Hamiltonian form with N+M degrees of freedom, where N degrees of freedom are
associated with the N charged particles interacting with M electromagnetic waves. The aim of this presentation is to show
that it is possible to influence by external perturbation the dynamics of the particles in order to enhance the stability of
the system resulting in a reduction of the oscillations of the waves. We apply a Hamiltonian control technique based on a
small and apt modification of the potential to recreate or break up invariant (KAM) tori in phase space. The core of our
approach is to locate local bifurcations (of periodic orbits) happening in the system as the parameters are varied. We show
that an appropriate tuning of the parameters is able to reduce by an order of magnitude the amplitude of the oscillations
without reducing the total power of the wave. This technique has been successfully implemented on a Travelling Wave Tube in
the test-particle regime [1].
References :
[1] C. Chandre, G. Ciraolo, F. Doveil, R. Lima, A. Macor, and M. Vittot "Channeling Chaos by Building Barriers", Phys. Rev.
Lett. 94, 074101 (2005)
[2] R. Bachelard, C. Chandre and X. Leoncini "Reducing or enhancing chaos using periodic orbits", preprint
[3] G. De Ninno and D. Fanelli, "Controlled Hopf Bifurcation of a Storage-Ring Free-Electron Laser", Phys. Rev. Lett. 92,
094801 (2004)
[4] C. Chandre, M. Vittot, G. Ciraolo, Ph. Ghendrih and R. Lima "Control of stochasticity in magnetic field lines", Nucl.
Fus. 46, 33 (2006)
6.Period-Doubling Oscilations And Chaos In CO Oxidation And Catalytic Mufflers
Miloš Marek, Dept. of Chemical Engineering, ICT Prague, milos.marek@vscht.cz
P. Koèí, ICT Prague
M. Kubíèek, ICT Prague
M. Schejbal, ICT Prague
Period-doubling oscillations and chaos in the course of CO oxidation on Pt/?-Al2O3 catalyst were observed experimentally
many years ago [1,2]. Interpretation of observed nonlinear dynamics was not possible at that time as proper non-stationary
kinetic relations were not available. The most common reactor, where the oxidation of CO and hydrocarbons takes place is
catalytic monolith used for automobile emission treatment, particularly the three-way converter (TWC). Mathematical models
and observations of TWC can also exhibit complex dynamic behaviour.
In this contribution an interpretation of experimental observations of hysteresis and oscillatory behaviour with transition
from simple periodic to chaotic regimes for carbon monoxide oxidation will be made. The results of bifurcation analysis [3]
of the lumped approximation of the three way catalytic converter using the non-stationary reaction kinetics [4] will be
described. The analysis predicts oscillations in the CO oxidation submodel based on nonstationary kinetics similarly as in
the full nonstationary kinetic model of the TWC converter. The used reaction network has been investigated by the use of
stoichiometric network analysis [5]. Major unstable reaction subnetworks underlying oscillations in the CO and hydrocarbon
oxidation have been identified. The nonlinear dynamics of CO oxidation in the lumped isothermal reactor model has been
analyzed in detail. The constructed evolution diagram confirmed the existence of hysteresis and oscillations. Continuation
software CONT [6] was then used to construct the dependence of solutions on parameters and the location of Hopf bifurcation
points.
Typical three-way catalytic converter is operated as a forced system, where the inlet oxygen concentration varies with a
frequency of approximately 1 Hz. Detailed analysis based on the use of continuation methods for analysis of periodically
forced systems revealed the existence of periodic, quasiperiodic and chaotic solutions. Arnold tongues in the parametric
plane frequency – amplitude of the inlet oxygen concentration have been constructed and related to time–averaged outlet
conversions of CO. Kinetic oscillations result in complex spatiotemporal patterns in the washcoat along the monolith.
Complex spatiotemporal patterns are also observed in spatially 2D mathematical model of TWC converter where the descriptions
of internal diffusion in the washcoat and axial heat conduction are included.
Nonlinear waves traveling in monolithic catalytic converters determine location and the time course of the converter
light-off and thus the time-averaged conversions of reaction components. It was found earlier in detailed experimental
investigations of spatiotemporal temperature patterns in the catalytic monolith [7] that highest conversion is achieved
when the light-off occurs close to the front part of the monolith. Simulations revealed that highest time-averaged outlet
conversions of emissions can be also achieved for aperiodic regimes at certain frequencies of inlet oxygen forcing.
References:
[1]J. Kapièka and M. Marek, Journal Catal., 1989a,119, 508-511.
[2]J. Kapièka and M. Marek, Surface Science, 1989b,222, L885-L889.
[3]M. Kubíèek and M. Marek, Computational Methods in Bifurcation Theory and Dissipative Structures, Springer, Heidelberg,
New York, 1983.
[4]P. Koèí, V. Nevoral, M. Záhrubský, M. Kubíèek and M. Marek, Chem. Eng. Sci., 2004,59, 5597-5605.
[5]I. Schreiber and J. Ross, Journal Phys. Chem. A, 2003,107, 9846.
[6]M. Marek and I. Schreiber, Chaotic Behaviour of Deterministic Dissipative Systems, Cambridge University Press, Cambridge,
1995
[7]R. Jahn, D. Šnita, M. Kubíèek and M. Marek, Catal. Today, 2001,70, 393-409.
7.Mixed-Mode Oscillatory Dynamics In A Ph-Oscillator
Igor Schreiber, Institute of Chemical Technology, Prague, Igor.Schreiber@vscht.cz
Daniel Bakeš, Institute of Chemical Technology, Prague
Lenka Schreiberová, Institute of Chemical Technology, Prague
Marcus Hauser, University of Magdeburg
The reaction of hydrogen peroxide, thiosulfate in acidic solution catalyzed by cupric ions (HPTCu reaction) displays rich
nonlinear dynamics displaying multiple steady states, excitability and oscillations in a continuous-flow stirred tank
reactor (CSTR) operated under isothermal conditions. The HPTCu reaction is a pH oscillator with variations of pH typically
in the range between 4 and 6. The reaction displays simple oscillations but in most of the oscillatory domain in the
parameter space complex oscillations occur. The waveform of these oscillations consists of a large-amplitude peak followed
by a series of small-amplitude oscillations. The length of the phase of small oscillations may vary in a regular or
irregular fashion. However, the purpose of the so far published measurements was to establish that the system is
oscillatory rather than systematically studying the transitions between various regular and irregular dynamical regimes. At
the same time, earlier experiments were done by using a peristaltic pump. This experimental arrangement does seem to
provide complex irregular oscillatory patterns but a question arises as to what is the effect of the peristaltic pump on
the complex patterns. Extensive experiments with the well-known Belousov-Zhabotinsky reaction made it clear, that the
periodic fluctuations in the inflow caused by the peristaltic pump – even if subtle – may significantly affect the dynamical
regime, and change it from simple oscillatory to complex oscillatory. In order to clarify this point and check the earlier
results, we have determined to use a large-volume syringe pump, which is able to deliver a nearly even inflow of the feed
solutions.
With this experimental setting, we present an investigation on the emergence of complex oscillatory dynamics. To this
purpose, both the flow rate of reactants (reciprocal residence time) and the inlet concentration of Cu2+ ions are
systematically varied. The transition from simple periodic oscillations to more complex oscillatory behaviour is presented
in more detail. Our preliminary results indicate that complex oscillatory patterns are indeed present in the system, and
that the transition to nonperiodic dynamics involves period doubling bifurcations. Also observed are multiple coexisting
dynamical regimes, which cause hysteresis in the system. The experimental data can be arranged into a bifurcation diagram
showing the regions of various oscillatory patterns and transitions (bifurcations) between them.
Although a mechanism has been published, if was found that it cannot describe the main features of the system accurately,
not to mention the rather subtle dynamical features that we observe experimentally. Recently, an attempt at a refined
mechanism has been made. We use these models to simulate the experimental findings and compare them against experiments and
each other.
8.The Influence Of Non-Stoichiometric On Viscosity Of The Fused Boric Anhydride
Michael Spiridonov, The Urals State Technical University-UPI, sma@mtf.ustu.ru
Vladimir Novikov, The Urals State Technical University-UPI
Non-stoichiometric compounds cause interest for research both from theoretical positions and their practical importance in
various areas of applied chemistry and metallurgy, at clearing semiconductor materials, welding of graphite and also
protection of metals against oxidation in particular. The samples for research were received as follows.
Pure B2O3 was sucelted in Al2O3-crucible in the furnace of resistance at 1473 K in an atmosphere of air and after two-hour
endurance and cooling transparent white glass of stoichiometric structure was received.
Replacing Al2O3-crucible on the graphite one at the same conditions opaque glass of boric anhydride with a gray-dark shade
of non-stoichiometric structure was received.
The experimental data on measurement of viscosity received by a method of vibrating viscometer melts have shown, that at low
temperatures viscosity of fused boric anhydride B2O3 which was exposed to interaction with a reducer (a graphite crucible)
is higher, than its viscosity measured in platinum crucible.
Thus, it is revealed, that at high temperatures viscosity of melt, which is in contact with a reducer, coincides with
viscosity of stoichiometric melt, and at low temperatures viscosity sucelted in graphite crucible oxide melt, being in
contact with a reducer, is much higher. The reason may be the presence of associates of a bivalent boron and oxygen
vacancies, and also the formation of a metal boron as suspension.
Thus, measurements of viscosity allow to reveal a degree of non-stoichiometric oxide melts.
9.The Matalon-Packter Law And Correlation Analysis Between Single- And Two-Salt Patterns In Periodic Precipitation Systems
Rabih Sultan, American University of Beirut, rsultan@aub.edu.lb
Farah Zaknoun, American University of Beirut
Periodic precipitation (or Liesegang) patterns present a variety of dynamical properties based on the inter-diffusion and
precipitation reaction of co-precipitate ions in a gel medium. A large variety of single salt systems has been the subject
of thorough studies, whereas multiple-salt investigations have been relatively scarce in the Literature.
In most Liesegang systems, it is known that the spacing between two consecutive bands increases with distance from the
gel-solution interface. By conducting spacing measurements on PbF2 and PbI2 Liesegang patterns in individual-salt
experiments, we attempt to predict the situation in a joint experiment involving the two precipitates simultaneously. In
other words we predict whether the PbF2 and PbI2 bands alternate or overlap. We then carry out experiments wherein the two
salts are precipitated in the same gel. The band content in the two precipitates (white PbF2 and yellow PbI2) is examined
visually, and determined by electrochemical analysis after re-dissolving the bands, using I- and F- specific electrodes. As
a result, a correlation assessment is established, between the band locations in the single-salt patterns, and the band
composition in the two-salt strata. A parameter to rigorously measure the described correlation is developed.
Finally the extent of correlation is mapped onto the applicability of the so-called Matalon-Packter law, which gives the
dependence of the band spacing coefficient on the initial concentrations of the co-precipitates.
10.On Chaotic Nature Of Speech Signals
Yuri Andreyev, Institute of Radioengineering and Electronics, yuwa@cplire.ru
Methods of nonlinear dynamics were used to study speech signals. These methods require sufficiently "long" signals, so we
studied those sounds that can be pronounced as long and stationary signals, such as vowels, some consonants (sibilants 's',
'sh'), and dual-nature sounds ('z').
As was found, all vowels can easily be embedded in a low-dimensional space, where they lay on subspace of dimension 3–4.
Typical, speaker-dependent spatial structures can be found in the embedding space. Thus, peculiarities of pronunciation of
different people can be treated geometrically, which gives rise to an idea of speech data banks for various applications.
Estimates of largest Lyapunov exponent proved to be positive for all studied sounds, which indicates the presence of chaos
in dynamic system of vocal tract and testifies to nonlinear (chaotic) dynamics of speech process.
11.Data Assimilation On Chaotic Dynamics
Haroldo Campos Velho, LAC-INPE, haroldo@lac.inpe.br
Rosângela Saher Corrêa Cintra, LAC-INPE
Helaine Furtado, LAC-INPE
Fabrício Pereira Härter, Waterloo Centre for Atmospheric Sciences
Data assimilation is an essential step for all operational process used to make predictions from a mathematical model. The
assimilation process is done by means of a weighted combination between observational and mathematical model data. Here,
data assimilation methods based on Kalman filter and artificial neural networks are applied to a non-linear systems under
chaotic regime.
12.Phase Space Embedding Of Trained And Non Trained Voice Signals: A Classification Problem
María Eugenia Dajer, Programa de Pós-Graduação de Interunidades em Bioengenharia. EESC. USP., medajer@sc.usp.br
José Carlos Pereira, Departamento de Engenharia Eletrica. EESC. USP.
Carlos Dias Maciel, Departamento de Engenharia Eletica. EESC. USP.
Human voice has been the focus of study for different areas of science. Researches in the last two decades have demonstrated
the existence of chaos in human voice production. The purpose of this work is to use a nonlinear dynamic technique, phase
space embedding, in the analysis of human voices from two different groups, healthy subjects with voice trained and healthy
subjects with non trained voice; and correlated them to traditional acoustic parameters as well as perceptual analysis.
Human voice signals from healthy subjects, both male and female, ranging in age from 19 to 39 years old were analyzed.
Sustained vowel sounds /a/, /e/ and /i/, from brazilian Portuguese were recorded at a sampling rate of 22,050 Hz and
analyzed in order to obtain acoustic measures (Jitter, Shimmer and coefficient of excess – EX). The phase space embedding
technique and Lyapunov Exponent were used to describe the nonlinear dynamic characteristics of the two groups of voice
signal samples. The results show, that non-linear dynamical method seems to be a suitable technique to discriminate voice
signals, due to the chaotic component of the human voice. It is suggested, that non-linear dynamic analysis does not
replace existing techniques instead, it may improve and complement the recent voice analysis methods available for speech
therapists and clinicians.
13.A Chaotic Analysis Of The Foreign Exchange Rates
Atin Das, Dr., dasatin@yahoo.co.in
Pritha Das, Dept. of Maths, BES University, Shibpur, Howrah, India
In this work, we investigate chaotic property of Foreign Exchange Rates of several countries. The foreign exchange market
is a 24-hour financial market. The trading in the foreign exchange markets generally involves the US dollar. Some of the
related earlier works found evidence of chaotic structures in foreign exchange rates (for example, in case of the Canadian
and Australian dollars over their floating rate periods), some studies found little evidence of chaos, however, many of
them showed evidence of nonlinear structure. This type of conflicting claims are common in nonlinear analyses of financial
data, as shown in our earlier work (AMC, 2005). For the present work, daily data were collected for thirteen countries,
mostly over the period January 1971 to December 2005. We have thus a time series of more than 8000 points for each country.
By measuring the largest Lyapunov exponent (LLE), we found indication of deterministic chaos in all exchange rate series. In
the present globalized economy, most countries accept pegging their currencies to the US dollar. Most of them are buying
the US dollar in order to curb the appreciation of their currencies. So, there are several types of interventions to control
exchange rates. To investigate that, we also calculate the ratio between the minimum and maximum values of exchange rate
during the period under study for each country and find it to be as high as 18 for SriLanka and as low as 2 for Singapore.
But LLE calculated for these countries do not reflect this important aspect. So we are lead to more fundamental question as
to what properties of a nonlinear time series are reflected by quantifying chaos in terms of LLE.
14.Study of heart rate variability using recurrence plots
Angela Maria dos Santos, Universidade Federal do Paraná, ansantos@fisica.ufpr.br
Ricardo Luiz Viana, Universidade Federal do Paraná
Sergio Roberto Lopes, Universidade Federal do Paraná
Moacir Fernandes de Godoy, Faculdade de Medicina de Rio Preto
In this work we have studied models of coupled oscillators through time series analyses to compares with laboratory data for
hear rate variability. We used recurrence plots for identifying dynamical relations between numerical models based on
oscillators and heart rate variability. We analysed both healthy and patological behaviors and we compared these behaviors
with dynamical regimes exhibited by coupled oscillators.
Besides recurrence plots some anothers aspects are verified, we have used entropy, determinism, laminarity and trapping time,
too.
15.Using Synchronization And Nonlinear Control In System Identification
Ubiratan Freitas, Laboratório Associado de Computação e Matemática Aplicada - Instituto Nacional de Pesquisas Espaciais,
ubiratan@lac.inpe.br
Elbert E. N. Macau, Laboratório Associado de Computação e Matemática Aplicada - Instituto Nacional de Pesquisas Espaciais
In dealing with experimental data, one is often faced with the problem of reconstructing the dynamical equations of the
system under study. This is the problem of system identification. To solve it is to find a mathematical model that can
reproduce the dynamical behavior observed on the system. This may be a rather difficult task, specially when dealing with
nonlinear systems. The usual approach for this problem is to employ a parametric model and an optimization technique to fit
the model's parameters to the data. In this paper, a different method is used. The identification is treated as a control
problem. Nonlinear geometric control and adaptive control techniques are employed to design a controller that can force the
model to synchronize with the data. As a by-product, the model's parameters are estimated in the process.
This method is applied to a nonlinear chaotic system as an example.
16.Recurrence Quantification Analysis As A Prognostic Tool For Imminent Death Diagnosis
Moacir Godoy, FAMERP, mfgodoy@netsite.com.br
Isabela Thomaz Takakura, HB-FUNFARME
Paulo Rogerio Correa, HB-FUNFARME
Emanuele Renata Tonolli, FAMERP
Raoni Tibiriçá Dantas, FAMERP
Flavio Correa Pivatelli, HB-FUNFARME
Common causes of death include infection (pneumonia and septicemia), organ failure (lungs, heart, liver, central nervous
system, or kidneys), infarction (lungs or heart), carcinomatosis or widespread metastatic disease and hemorrhage. In all
these conditions homeostasis is lost. When this occur is common a net reduction in the heart rate variability. Heart rate
variability (HRV) parameters have been used to predict risk in patients with structural heart diseases or other pathological
states and also to characterize the normal functional condition of the autonomic nervous systems from childhood to
senescence. It is possible to study the HRV with the aid of the traditional linear parameters but they only provide limited
information about the underlying complex system. The recurrence quantification analysis (RQA) is an alternative tool to
quantify the complexity even in rather short time series being independent of limiting constraints such as data set size,
data stationarity, and assumptions regarding statistical distributions of data. The RQA methodology is fully applicable to
any rhythmical system, whether it be mechanical, electrical, neural, hormonal, chemical or even spatial. So, the aim of the
present study was to investigate how RQA behaved in a group of patients in which the death was imminent compared to patients
with a condition that was not so critical. Casuistic and Methods: Were included 155 patients, 25 who died in a short time
after RQA (Group A) and 130 that stayed alive for long time (Group B). In all the patients were studied time series of 1,000
beat-to-beat RR intervals (captured with the aid of Polar Advantage S810i equipment). The variables studied were Recurrence
Rate and Determinisn. The used software was available at http://www.agnld.uni-potsdam.de/~marwan/rp/rp_www.php Results: Mean,
Standard Deviation and Median for Recurrence Rate in Group A were respectively 0.050745, 0.049180 and 0.032774. Mean,
Standard Deviation and Median for Recurrence Rate in Group B were respectively 0.012355, 0.008087 and 0.009856. For
Determinism the values were 0.196332, 0.118851 and 0.218147 for Group A and 0.059329, 0.050093 and 0.040010 for Group B. For
the Recurrence Rate the best cut-off value was 0.013439 and for Determinism the best cut-off value was 0.184421. So, for
the Recurrence Rate variable the ODDS Ratio was 23.419 (CI95% =6.6 to 83.6; P<0.0001) and for the Determinism variable ODDS
Ratio was 75.3(CI95% = 18.4 to 307.2; P<0.0001). Conclusion: Recurrence Rate and Determinism are excellent markers of
imminent death, so Recurrence Quantification Analysis can be suggested as a prognostic tool in medical activities.
17.Applying Chaos in Patrol Missions of Mobile Robots
Luiz S. Martins-Filho, Universidade Federal de Ouro Preto, luizm@iceb.ufop.br
Elbert E.N. Macau, Instituto Nacional de Pesquisas Espaciais
Ronilson Rocha, Universidade Federal de Ouro Preto
This work introduces a path planning strategy for mobilerobots based on dynamical features of chaotic systems. This peculiar
methodology of constructing trajectories envisages missions for terrain exploration, with specific purpose of search or
surveillance. The proposed way to achieve fast scanning of the robot workspace consist of a scheme of imparting a chaotic
motion behavior to the mobile robot using a path-planner based on the conservative Standard map. As a consequence, for a
external observer, the robot trajectories resemble highly opportunistic and unpredictable, with characteristics that
quickly scans the surveillance space.
18.New Global Vector Field Reconstruction From A Chaotic Time Series In Copper Electrodissolution
Jean-Marc Malasoma, Laboratoire Géomatériaux - ENTPE - DGCB URA CNRS 1652, malasoma@entpe.fr
Marie-Aurélie Boiron, Laboratoire Géomatériaux - ENTPE - URA CNRS 1652
Jack Hudson, Department of Chemical Engineering, University of Virginia
Chaotic oscillations have been observed in a number of electrochemically reacting systems. We are interested in the
development of ad hoc mathematical models directly from the experimental data in order to characterize and predict the
system dynamics, and also to increase the understanding of its dependence on parameters.
We used an experimental time series obtained by J.L. Hudson and co-workers from dissolution current measurement during the
potentiostatic electrodissolution of a rotating Cu electrode in phosphoric acid. It has been known for some time that
oscillations can occur in this system, and an extensive study of its dynamics has been carried out by Shell and co-worker
who showed the existence of Hopf bifurcation, period doublings to chaos, alternating periodic and chaotic states, Farey
sequences of mixed-mode oscillations, etc.
After the initial transient signal disappeared, the behavior settles down to a chaotic attractor. We proved that such an
attractor may be reconstructed in a 3D space spanned from the current time series and its two successive time derivatives.
Then by using a new recently developed method of global vector field reconstruction, we obtained a set of three differential
polynomial equations which models the experimental data.
Our model contains 26 monomials of maximal degree 3, and therefore it is much more simple than the model obtained ten years
ago by Letellier and co-workers which contains 52 terms of maximal degree 5. This new model is very robust and is checked by
topological characterization, which gives identical templates for the experimental attractor reconstructed with successive
derivatives and the chaotic attractor generated by numerical integration. The model is therefore topologically compatible
with the experimental data.
A very accurate study of the population of periodic orbits related to the experimental and numerical chaotic attractors is
given. Finally, numerical bifurcation diagrams, related to various control parameters of the model, are compared with the
observed experimental route to chaos.
19.On The Prediction Of Chaotic Time Series Using The NARX Recurrent Neural Network: A New Approach
José Maria Menezes, Federal University of Ceará, josemenezesjr@yahoo.com.br
Guilherme A. Barreto, Federal University of Ceará
The NARX network model is a recurrent neural architecture commonly used for input-output modeling of nonlinear systems. The
input regressor of the NARX network is formed by two tapped-delay lines, one sliding over the input signal and the other
one over the output signal. When applied to chaotic time series prediction, the NARX network is usually designed as a plain
Nonlinear Autoregressive (NAR) model by eliminating the output's delay line. In this paper, we propose a simple but
efficient strategy to allow the NARX network to fully exploit input and output delay lines to improve its prediction
performance. We use the laser data of the Santa Fe Competition to evaluate the proposed approach in multi-step-ahead
prediction tasks. The results show that the proposed approach consistently outperforms standard neural network based
predictors, such as the TDNN, Elman and FIR-MLP.
20.Use Of The Liapunov Exponents In The Analisys Of Disturbances In Var Furnace Dc Electric Arc
Cristiano Mucsi, Instituto de Pesquisas Energéticas e Nucleares, csmucsi@ipen.br
Jesualdo Luis Rossi, Instituto de Pesquisas Energéticas e Nucleares
Vacuum arc remelting furnaces are devices typically used for the melting of refractory and reactive metals and alloys. The
VAR operational characteristics yield unique metallurgical properties to its products which have applications mainly in the
nuclear and aero spatial industry. This work presents the evaluation of observed oscillations in the DC voltage of electric
arcs in a prototype VAR furnace. The invariants of the reconstructed space state were evaluated and its evolution was
assigned to the melting dynamics (melting; droplet growing and separation). The results show that the electric arc
dynamical system exhibits a chaotic behaviour and that the Liapunov exponent varies during the formation and separation of
the liquid metal droplets cyclic events. The cyclic variation of the Liapunov exponents is then related to the evolution of
the electro-hydrodynamic phenomena within the melting process.
21.Measuring Variability In Economical Data
Jose Roberto Castilho Piqueira, Departamento de Engenharia de Telecomunicações e Controle, Escola Politécinica de
Universidade de São Paulo, piqueira@lac.usp.br
FA Serboncini, Poli / USP
LHA Monteiro, Poli / USP
This essay proposes some mathematical methods to analyze the variabilty of economical data. The idea is to express the
state of an economical system as a linear combination of base states in a Hilbert space. Coefficients of the linear
combination can be interpreted as probabilities and informational entropy is associated to each state, giving hints about
the dynamics of the system structure. Besides, state transition matrices can also be calculated and their norms express the
dynamics of the system functional evolution.
22.Fractal Analysis Of Different Eastern And Western Musical Instruments
Das Pritha , Dept of Mathematics, BES University, prithadas01@yahoo.com
Atin Das, NH School
In this paper, we attempt musical analysis by measuring fractal dimension (D) of musical pieces played by several musical
instruments. We collected solo performances of popular instruments of Western and Eastern origin as samples. We attempted
usual spectral analysis of the selected clips to observe peaks of fundamental and harmonics in frequency regime. After
appropriate processing, we converted them into time series data sets and computed their fractal dimension. Based on our
results we conclude that instrumental musical sounds may have higher Ds than those computed from vocal performances of
different types of Indian songs.
23.Multifractal Surface Analysis Of A Laser Beam Melt Ablation Process
Camilo Rodrigues Neto, University of São Paulo, camiloneto@usp.br
Kevin Bube, University of Oldenburg, Germany
Reik Donner, University of Potsdam, Germany
Udo Schwarz, University of Potsdam, Germany
Ulrike Feudel, University of Oldenburg, Germany
We study the properties of surfaces generated by a laser beam melt ablation (LBMA) process. We present the analysis and
ordering of the surfaces depending on the adjusted process parameters. Our findings give some insight in the performance of
two widely applied multifractal analysis methods – the detrended fluctuation analysis (DFA) and the wavelet transform
modulus maxima (WTMM) method -- on short real world data.
24.Detection Of The Coupling Direction By Means Of Recurrences
Maria Carmen Romano, University of Potsdam, romano@agnld.uni-potsdam.de
Marco Thiel, University of Potsdam
Juergen Kurths, University of Potsdam
We propose an index based on recurrences in phase space for the detection of the directionality of the coupling between two
systems. The main advantage of this recurrence based index is that it is applicable to time series, even when they are
strongly contaminated by observational or dynamical noise.
We compare the newly proposed index with known techniques to detect the directionality of the coupling, such as the
phase-based and conditional entropy methods.
25.Characterization Of Chaotic Deterministic Dynamics In Atmospheric Time Series
Andriana S. L. O. Campanharo, LAC/INPE, andriana@lac.inpe.br
Elbert E. N. Macau, LAC/INPE
Fernando M. Ramos, LAC/INPE
Recently, developments in computer technology and applied mathematics have allowed an improved understanding of nonlinear
chaotic phenomena. However, the proper characterization of chaotic deterministic dynamics from noisy, real-world data can
still be a challenge. Here we review of some of the main numerical tools for nonlinear time-series analysis, and highlight
problems and limitations when dealing with experimental data. For this, we use high-resolution atmospheric temperature data
measured in a 66m micrometeorogical tower, during a field campaign of the Large-Scale Biosphere-Atmosfere Experiment in
Amazonia.
26.D-Infinite PARAMETER TO EXTRACT SPATIO-TEMPORAL FEATURES IN MEG DATA
Francesca Sapuppo, Dipartimento di Ingegneria Elettrica, Elettronica e dei Sistemi, Universita' degli Studi di Catania,
fsapuppo@diees.unict.it
Elena Umana, Dipartimento di Ingegneria Elettrica, Elettronica e dei Sistemi, Universita' degli Studi di Catania
Mattia Frasca, Dipartimento di Ingegneria Elettrica, Elettronica e dei Sistemi, Universita' degli Studi di Catania
David Shannahoff-Khalsa, Institute for Nonlinear Science, University of California, San Diego
Luigi Fortuna, Dipartimento di Ingegneria Elettrica, Elettronica e dei Sistemi, Universita' degli Studi di Catania
Maide Bucolo, Dipartimento di Ingegneria Elettrica, Elettronica e dei Sistemi, Universita' degli Studi di Catania
Introduction: We exploit the potentiality of the dinfinite parameter for data analysis enhancing the method to evaluate it
and overcoming the calculation of the embedding space dimension. In particular this approach has been used to analyze
magnetoencephalography (MEG) signals.
Material and Methods: The value of dinfinite characterizes the system’s asymptotic chaotic behavior and it can be
calculated from the dj that is defined as the average distance between trajectories that start from very close initial
conditions [1]. The evaluation of this parameter has been already adopted in literature in relation with the well known
Chua chaotic system [2].
The developed numerical algorithm implements the theoretical calculation of the dj and its asymptotic value dinfinite given
an experimental time series x(t). Trajectories (xj ) starting from a point included in the boundary with radius d0 of a
given x* initial condition (x*± d0) are extracted.
The processing for the calculation of the dj is performed using pairs (xi, xi’ ) of selected trajectories that meet
specifically conceived constrains on parameters such as initial slope, length in time of the considered trajectories and the
minimum distance in time between the trajectories. The initial slopes of xi and xi’ must agree in sign and have to be close
in value within a fixed tolerance. The length of the trajectories is fixed in a way that both the stretching and the
folding effects are taken into account and the asymptotic behavior of the system can be studied. The average dj of the
trajectory distances is then performed and the dinfinite, which represents the average of the asymptotic value of dj, is
extracted.
This implementation, taking into account the over mentioned constrains, circumvents calculating the embedding space
dimension, which can be computationally onerous. Moreover, being space-dimension independent makes the dinfinite algorithm
general, in a way that it can be used for the characterization of time series coming from measurements performed on real
systems also when the laws and structures are unknown and chaotic dynamics are suspected. It is furthermore important to
notice that, while the Lyapunov exponent (LE) in the study on chaotic dynamics is only sensitive to the stretching
mechanism between nearby starting trajectories, the dinfinite is sensitive to both the stretching and the folding
mechanisms [1][2]. Therefore, the dinfinite could be an important measure for the characterization of chaos when the LE is
not computed, or to distinguish between series which have the same Lyapunov exponent.
Results and Conclusions: The algorithm is applied to whole-head 148 channel MEG data during a structured yogic breathing
meditation technique. The subject was recorded while reclining and supported at 45 degrees. The subject followed a
well-practiced protocol that involved 10 min of resting baseline recording (Rest phase 1), followed by an Exercise phase
that included 31 min, and again followed by 10 min of rest (Rest phase 2). The Exercise phase consists of selectively
breathing through only one nostril (using a plug for the other one) at a respiratory rate of one breath per minute (15 s
slow inspiration, 15 s breath retention, 15 s slow expiration, and 15 s breath hold out) [3]. This procedure is performed
in order to capture the residual effects on the brain activity due to the two possible types of breathings using either
the left or right nostril.
A spatio-temporal distribution of the dinfinite on the digitalized representation of the head map is calculated on the
normalized MEG signals coming from the complete protocol of meditation technique. The signals were normalized to make the
analysis independent from their power.
Dramatic differences between the dinfinite distributions on the head map during the three different phases arise; they were
not clearly featured in the power spatio-temporal distribution [3].
We propose the dinfinite characterization as a promising and convenient method that can be used as a complementary method to
the conventional characterization of the MEG signals in order to enlighten spatial and temporal patterns in the brain
activity.
References:
[1] Strogatz S. H., “Nonlinear Dynamics and Chaos”, Perseus Book, Cambridge, Massachusetts. Webster J.G. (1998), Medical
Instrumentation, Wiley
[2] Bonasera A., Bucolo M., Fortuna L., Frasca M., Rizzo A., ‘A New Characterization of Chaotic Dynamics: the d-infinite
Parameter’ (2003), Nonlinear Phenomena in Complex Systems, 6, No 3, pp. 779-786 - Education and Upbringing Publishers,
National Accademy of Science Belarus and Belarusian State University
[3] Bucolo M., La Rosa M., Frasca M., Fortuna L., Shannahoff-Khalsa D., DS, Schult, R.L, and Wright, J.A (2001)
“Independent Component Analysis of Magnetoencephalography Data”, Conference of IEEE Engineering Medicine and Biology
Society (EMBC 01), Istanbul.
27.Ensemble Approach For Recovering Phase Synchronization From Experimental Time Series
Isao Tokuda, Japan Advanced Institute of Science and Technology, +81-761-51-1226
Ulrich Parlitz, University of Goettingen
Alexander Hlborn, University of Goettingen
Juergen Kurths, University of Potsdam
An ensemble approach is presented for the reconstruction of a phase synchronization diagram from time series. As an example
system, we first analyze the forced Roessler oscillator to show that synchronization diagram reconstructed by conventional
method using a single nonlinear model depends sensitively upon the model parameters, which should be estimated with a
considerable amount of care. This dependence can be crucial for a precise recovery of the synchronization phenomena.
To overcome this weakness, an ensemble approach is introduced. Two types of techniques, namely, (I) ensemble regression
and (II) ensemble classification, are developed to show that they provide much more robust and reliable reconstruction of
the synchronization diagram compared to the conventional single modeling approach. To demonstrate significance of this new
approach, we apply it to experimental systems including lasers and electronic circuits.
28.Experimental Chaotic Semiconductor Laser – Wide Measurement Bandwidth Chaos Analysis
Joshua Toomey, Macquarie University, jtoomey@ics.mq.edu.au
Deborah Kane, Macquarie University
Using wide bandwidth detectors and real-time oscilloscopes with multiple Megabyte memory capacity it is now possible to
collect large data sets of chaotic output power from chaotic semiconductor lasers (CSL) at bandwidths up to ~6 GHz. We
present analysis of the chaotic output power time series produced experimentally by a CSL based on a semiconductor laser
with optical feedback system. The key indicator used to date, to characterize the complexity is the correlation dimension.
The effect that experimental signal-to-noise ratio has on correlation dimension estimates has been measured and experimental
system parameters that allow robust correlation dimension results have been determined. High levels of noise are shown to
compromise any estimate of the correlation dimension. The measurement bandwidth has also been shown to greatly affect the
correlation dimension. A lower detection bandwidth results in exclusion of the complex higher frequency dynamics and
consequently leads to lower estimate of dimension.
The correlation dimension as a function of embedding dimension has been measured for simultaneously collected output power
time series from a synchronized transmitter/receiver pair of CSLs. The two synchronised CSLs have quite different noise but
it has been shown that the correlation dimension graph of each of the transmitter and receiver laser outputs is identical
for a cross correlation coefficient of the synchronized chaos above 0.9. Differences in the CD graph emerge as the cross
correlation coefficient is reduced.
29.The Complex Behavior Of A Slightly Modified Van Der Pol Circuit
Ruy Barboza, University of Sao Paulo at Sao Carlos, rbarboza@sel.eesc.usp.br
A simple van der Pol circuit consists of a tank circuit combined with a resistor with a cubic shaped nonlinearity. In our
experiments the nonlinear resistor was constructed with two diodes and a negative linear resistor. To produce van der Pol´s
relaxation oscillations of the hard type at low frequencies we used capacitances and inductances in the range of tens to
hundreds nanofarads and millihenries, respectively. We observed that the simple oscillatory behavior of the circuit can be
drastically changed if a small inductance coil is added in series with one of the two diodes. Typically, neuron-like spikes
and bursts appear. By varying the circuit parameters the voltage and current waveforms can be largely modified and complex
phenomena such as bifurcations and chaos are observed. Although the circuit topology was only slight modified, the
resulting system seems difficult to be modeled in detail. However, many phenomena are qualitatively reproduced using an
approximate model. In this work we present the circuit and it mathematical description, along with numerical and (mainly)
experimental results showing a variety of regular and chaotic waveforms, bifurcation diagrams and Poincaré maps.
30.Anticipation Enhances Synchronization Quality
Jonathan Blakely, US Army RDECOM, jonathan.blakely@us.army.mil
Ned Corron, US Army RDECOM
Shawn Pethel, US Army RDECOM
We report a surprising enhancement of synchronization quality between two chaotic oscillators coupled through a noisy
channel. We observe this effect experimentally in a pair of chaotic radio frequency Lorenz-like oscillators. A coupling
circuit injects a current into the response oscillator proportional to the difference between the current state of the
drive and a delayed state of the response producing anticipating synchronization. We record the average synchronization
error as a function of the anticipation time. Noise injected into the coupling degrades the fidelity with which the
response can reproduce the drive waveform. However, as we increase the anticipation from zero, the observed error decreases
and the synchronization quality is thus enhanced before loss of stability occurs. We observe similar enhancement in
simulations of other chaotic systems. These observations suggest that introducing a delay in coupling may be a widely
applicable strategy for improving synchronization quality in the presence of noise.
31.Swarm-Fuzzy Modeling Applied To Identification Of Chua's Circuit System
Leandro dos Santos Coelho, Pontifícia Universidade Católica do Paraná (PUC-PR) , andro.coelho@pucpr.br
Ernesto Araujo, Instituto Nacional de Pesquisas Espaciais – INPE
Fuzzy modelling of Chua's nonlinear circuit through particle swarm optimization (PSO) based on experimental results is
presented and discussed in this paper. Chua's circuit consists of an electronic chaotic oscillator and presents the
advantadge that it has been used as platform of tests in many areas related to the study of the chaos, telecommunications,
cryptography and physics. One of the key problem in system identification is to find out a suitable mathematical model of
dynamic system based on measured data. In general, the construction of mathematical models to forecast a nonlinear and
chaotic time series is not a simple task. In recent years, the interest in the identification strategies of nonlinear
systems with chaotic behavior reappeared, many of these using fuzzy systems in synergetic manner with softcomputing
techniques. The objective of this optimized fuzzy model is to find out a chaotic behavior based on experimental results
allowing the construction of mathematical models. In so doing, the fuzzy approach and particle swarm optimization working
in cooperation are an alternative to surpress the difficulties when dealing with chaotic time series identification.
32.Bursting In Physical System
Syamal Dana, Indian Institute of Chemical Biology, Kolkata, skdana@iicb.res.in
Bursting oscillation is seen in many slow-fast dynamical systems. Many bursting models using continuous flow and maps are
available. The basic idea is to control fast oscillations periodically by a slow motion. The dynamics thus switches between
an oscillatory state to a quiescent state either periodically or irregularly. The quiescent state again may be an
equilibrium state (rest state) or a small amplitude oscillation (sub-threshold oscillation). The bursting is called
point-cycle bursting for a quiescent state at rest while it is called cycle-cycle bursting if the quiescent state is a
small amplitude oscillation. More strict definition of bursting is proposed in terms of two important bifurcations, one
during switching from quiescent state to oscillatory state followed by another during oscillatory state to quiescent state.
Neurons are usually classified as integrator or resonator depending upon the type of bifurcation during their transition to
limit cycle oscillation from the excitable state, namely, saddle-node bifurcation (integrator) and Hopf bifurcation
(resonator).
We present here examples of two physical systems, namely, RCL-shunted Josephson junction model and Chua oscillator which
show saddle-node and Hopf bifurcation respectively during their transition to limit cycle oscillation from excitable state.
The Josepshon junction, in our numerical simulation, shows parabolic bursting when forced by an external slower periodic
oscillation. The Chua oscillator also shows parabolic bursting near homoclinic bifurcation when forced by an external
periodic motion with much lower frequency than its unforced oscillation. However, in the autonomous Chua oscillator, when a
system parameter is tuned near the homoclinic bifurcation it shows cycle-cycle chaotic bursting. This is due to merging
[1,2] of stable and saddle cycles. The results in the Chua oscillator are verified both in numerical simulation and in
physical experiment.
Such cycle-cycle bursting can be seen in any other reflection symmetric system like modified Van der Pol oscillator [2]
where one can find such merging of saddle and stable cycle.
References:
[1] P.K.Roy, S.K.Dana, Gluing bifurcation in Chua oscillator, Int.J.Bifur. and Chaos (in Press).
[2] P.Glendinning, Imperfect Gluing Bifurcation, Phys. Rev. E 64, 036208 (2001).
[3]M.Golubitsky, L.Shiau, Bursting in Coupled Cell system, preprint
33.Multi-Step-Ahead Forecast Of Chaotic Systems Based On Radial Basis Function Neural Network Using Particle Swarm Training
Leandro dos Santos Coelho, Pontifical Catholic University of Parana, leandro.coelho@pucpr.br
Fabio Alessandro Guerra, LACTEC - Institute of Technology for Development
Julio Cezar Zanoni, TECPAR – Parana Institute of Technology
The chaos theory aims the study of diverse pertinent phenomena to the nonlinear dynamic systems, such as bifurcations,
couplings between variables and variant parameters in time. Through the chaos theory it is possible to analyze diverse
apparently unexpected phenomena, searching for hidden patterns and simple laws running on complex dynamic behaviors. The
behavior of a chaotic system can be evaluated through the methodologies configuration of nonlinear identification systems
[1], [3], [7].
System identification, which is excellent area in many fields of knowledge, is the procedure to identify a model of an
unknown process, for prevision intentions and/or understanding the process behavior. The inherent complexity of many real
processes (nonlinear and variant in time) makes it difficult to apply conventional identification techniques. This aspect
has motivated the development of advanced identification techniques based on computational intelligence approaches, which
the neural networks, the evolutionary algorithms and fuzzy systems [2], [4], [6].
The use of neural networks to nonlinear identification problems has attracted some attention in recent years. Neural
networks are originally inspired by biologic neural networks’ functionality that may learn complex functional relations
through a limited number of training data. Neural networks may serve as black-box models of nonlinear multivariable dynamic
systems and may be trained using input-output data, observed from the system [5], [6]. The usual neural network consists in
multiple simple processing elements, called neurons, interconnections among them and the weights attributed to the
interconnections. The relevant information of such methodology is stored in the weights [7].
An alternative approach, among many others, for mathematical representation of dynamic systems with complex or chaotic
behavior, is a radial basis function neural network using k-means and fuzzy c-means for clustering and optimized by
pseudo-inverse and particle swarm optimization. This paper presents the implementation and study to identify three
dynamic systems, with nonlinear and chaotic behavior, called Rössler’s circuit, Chua’s circuit, and Lorenz’s attractor,
with concepts of multi-step-ahead prediction. For the Chua’s circuit the used data had been removed of its electronic
circuit. On other side, the data of the Rössler’s circuit had been simulated in the Electronic Workbench (EWB). Finally,
the Lorenz's attractor used data from its equations, simulated in Matlab computational environment.
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4, pp. 364-378, 1971.
[2] Ioh, M.; Yang, T.; and Chua, L. O. Conditions for impulsive synchronization of chaotic and hyperchaotic systems,
International Journal of Bifurcation and Chaos, vol. 11, no. 2, pp. 551-560, 2001.
[5] Alligood, K. T.; Sauer, T. D.; and Yorke, J. A. Chaos: an introduction to dynamical systems, Springer, 1996.
[6] Ljung, L. System identification: theory for the user. Prentice-Hall: New York, 1987.
[7] Mcloone, S.; Brown, M. D.; Irwin, G.; and Lightbody, A. A hybrid linear/nonlinear training algorithm for feedforward
neural networks. IEEE Transactions on Neural Networks, vol. 9, no. 4, pp. 669-684, 1998.
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Transactions on Neural Networks, vol. 1, no. 1, pp. 4-27, 1990.
[9] Pei; W.; Yang; L.; and Z. He. Identification of dynamical noise levels in chaotic systems and application to cardiac
dynamics analysis, International Joint Conference on Neural Networks, IJCNN, vol. 5, Washington, DC, USA, pp. 3680-3684,
1999.
34.Estimating Chaotic Orbits Generated By Maps With Nonuniform Invariant Density
Marcio Eisencraft, Mackenzie Presbyterian University , marcioft@mackenzie.br
Luiz Antonio Baccalá, Polytechnic School of the University of São Paulo
The estimation of chaotic orbits is an important aspect for the practical implementation of chaotic digital modulation
schemes without chaotic synchronization. In this context, Dedieu and Kissel (1999) proposed a Viterbi estimation algorithm
for chaotic orbits generated by one-dimensional maps under additive white gaussian noise.
In this paper, we show that the latter algorithm has considerable estimation gain only for generating maps whose invariant
density (Lasota and Mackey, 1985) is uniform. Using a convenient partition of the domain, we present a generalization that
provides high estimation gain to orbits of a broader class of maps. We just require that the generating map has a known
conjugation with a uniform invariant density map. Three aspects of the performance of the modified algorithm are
investigated: (1) the number of points used in the estimation; (2) the number of quantization intervals and (3) the Lyapunov
exponent of the orbit.
The attained gain is compared to that obtained via the maximum likelihood estimator (MLE) proposed by Papadopoulos and
Wornell (1993). The generalized Viterbi estimation algorithm achieves larger estimation gain (as much as 5dB in some
situations) in spite of introducing significant quantization errors.
References
[1]DEDIEU, H.; KISEL, A. Communications with chaotic time series: probabilistic methods for noise reduction. International
Journal of Circuit Theory and Applications, v. 27, p. 577-587, 1999.
[2]LASOTA, A.; MACKEY, M. Probabilistic properties of deterministic systems, Cambridge: Cambridge University, 1985.
[3]PAPADOPOULOS, H. C.; WORNELL, G. W. Optimal detection of a class of chaotic signals. In: IEEE CONFERENCE ON ACOUSTIC,
SPEECH AND SIGNAL PROCESSING, Minneapolis, 1993. Proc. ICASSP’93, v. 3, p. 117-120, 1993.
35.Synthesis Of Rössler-Like Dynamic In Electronic Circuits: A Piecewise Approach.
Gleison Fransoares Vasconcelos Amaral, Universidade Federal de São João del-Rei, amaral@ufsj.edu.br
Luis Antonio Aguirre, Universidade Federal de Minas Gerais
Erivelton Geraldo Nepomuceno, Universidade Federal de São João del-Rei
Paulo Monico Júnior, Universidade Federal de São João del-Rei
Carlos Eduardo Pádua Oliveira, Universidade Federal de São João del-Rei
This work presents an approach to synthesize the Rössler-like dynamic in electronic circuit using piecewise models. The
first step is the determination of a piecewise affine model to the system. The switching surface determination of the model
is based on topology of the chaotic attractor. Topological analysis is used to fine tuning and validation.
After that, the model is rebuilt using a modulus function. This function permits to codify switching and local dynamic of
the system. This function describes the dynamic in a compact way and makes the implementation of an electronic circuit
easier.
However, as the representations are not equivalent, except in only one point, it is investigated on the parameter space,
regions that represent equivalence. For that, the switching surface is parameterized and can be considered as bifurcation
parameter. Another parameter of the original system is used to realize a search in the parameter space. The resultant model
is simple and presents only two sub-models. The topology of the resultant model is validated by means of a topological
analysis.
Once determined the model that uses the modulus function and the parameter space regions, the circuit is implemented.
Experimental results prove the developed procedure. The behaviors of the model are verified in the circuit. Among the
regimes observed experimentally are, period-3, unimodal and multimodal chaos.
36.A Measurement System Based On Synchronization Of Two Chaotic Systems
Mattia Frasca, University of Catania, mfrasca@diees.unict.it
Luigi Fortuna, University of Catania
Salvatore Graziani, University of Catania
In this paper, a measurement system based on synchronization of two chaotic systems is introduced. The measurement system
uses a comparison technique. Like in the most known example of comparison measurement systems (i.e. the balance), two arms
(one containing the element to be measured and the other one containing the reference element of known value) have to be
considered and the equilibrium has to be evaluated. The arms of our system are represented by two chaotic systems which
differ only by the value of one element. The equilibrium is evaluated by considering the synchronization error of the two
systems. In fact, in the adopted scheme, the two systems are connected in a master-slave configuration: when the measured
element and the reference element are equal, the two chaotic systems are perfectly synchronized. Otherwise, when measured
element and the reference element are not equal (i.e. when master and slave do not have the same parameters), the two
chaotic systems do not synchronize. In this case, a parameter of the master circuit is varied to reach the equilibrium;
once reached the equilibrium, the measure of the element of unknown value is given by the master parameter value. An
experimental characterization of the system has been carried out. In particular, the system has been applied to measure the
value of an unknown resistor.
37.Experimental Evaluation Of Synchronization Quality In Coupled Chaotic Circuits
Edgar Furtado, Universidade Federal de Minas Gerais, edgar@cpdee.ufmg.br
Leonardo A. B. Tôrres, Universidade Federal de Minas Gerais
Luis Antônio Aguirre, Universidade Federal de Minas Gerais
The synchronization between Chua's circuits, connected in a master-slave configuration, is explored in order to investigate
two separate but complementary issues, namely: (i) which is the best state variable to be transmitted from the master to
the slave system, in the sense that the coupling strength is minimized; and (ii) in what way the parameter mismatch between
the master and slave oscillators affects the synchronization quality, considering that the systems are coupled based on the
transmission of different state variables. To accomplish this study, it is employed an experimental setup, called PCChua,
which is composed by one data acquisition and analog output board, a microcomputer running free and open source real-time
control and data acquisition software, and a very slow inductorless Chua's circuit, enhanced with electronic actuators.
Another goal of this work is to present this low cost experimental platform as an easy to copy and reproduce setup, that
can be extensively used on practical research on chaos theory.
38.Coherent Regimes Of Mutually Coupled Chua’s Circuits
Iacyel Gomes da Silva, Instituto Mediterráneo de estudios Avanzados IMEDEA (CSIC-UIB), iacyel@imedea.uib.es
R. Toral, Instituto Mediterráneo de estudios Avanzados IMEDEA (CSIC-UIB)
S. De monte, Dept. of Biology UMR 7625, Ecole Normale Supérieure, Paris, France
F. d Ovideo, Lab. De Métérologie Dynamique, UMR 8539, Ecole Normale Supérieure, Paris France
C. R. Mirasso, Departament de Física, Universitat Illes Balears
We study dynamical regimes that emerge from the strongly coupling between two Chua’s circuits with parameters mismatch. For
the region around the perfect synchronous state we show how to combine parameter diversity and coupling in order to robustly
and precisely target a desired regime. This target process allows us to obtain regimes that may lie outside parameter
ranges accessible for any isolated circuit. The results are obtained by following a recently developed theoretical technique,
the order parameter expansion, and are verified both by numerical simulations and on electronic circuits. The theoretical
results indicate that the same predictable change in the collective dynamics can be obtained for large populations of strongly
coupled circuits with parameter mismatches.
39.Analysis Of A New Chaotic Sequence For Fast Spread Spectrum System
Junrong Gu, Electronic and Information Engineering School of Dalian University of Technology, gu_autumn@126.com
Minglu Jin, Electronic and Information Engineering School of Dalian University of Technology
This paper proposes a novel chaotic sequence generating fast algorithm which reduces the qualification influence in
generating finite length sequence. The fast algorithm possesses both efficiency and security merits. Based on a new
chaotic mapping with infinite collapse, its property and performances are discussed, and compared with other chaotic
sequences. The finite precision threshold is also investigated as to generate sequence practically.
40.Secure Communication With Chaotic Circuits Using Two Channels
Rider Jaimes, Centro Universitario de Los Lagos, Universidad de Guadalajara, rjaimes@culagos.udg.mx
Roger Chiu Zarate, Centro Universitario de Los Lagos, Universidad de Guadalajara
J. H. García-López, Centro Universitario de Los Lagos, Universidad de Guadalajara
Alexander N. Pisarchik, Centro de Investigaciones en Optica
Danuard Medina , Centro Universitario de Los Lagos,Universidad de Guadalajara
Rocio Ramirez, Centro Universitario de Los Lagos,Universidad de Guadalajara
We present experimental results on secure communications based on chaotic Rössler electronic circuits using two channels.
Each electronic circuit, transmitter and receiver, has three channels corresponding to three variables: x, y, and z. The
circuits are unidirectionally coupled by one of the channels (y), while a signal of information is transmitted through
another channel (x). Since the coupled channels are identical, the error in synchronization is much lower than that in
conventional communication schemes. We demonstrate experimentally the applicability of our approach for secure communications
by sending audio messages.
41.Practical Issues On Robust Chaos Synchronization Applied To Secure Communications
Eduardo Mendes, Department of Electronics Engineering - Federal University of Minas Gerais - UFMG, emmendes@cpdee.ufmg.br
Claudio Campos, Department of Electronics Engineering - PUC/Minas
Reinaldo Palhares, Department of Electronics Engineering - Federal University of Minas Gerais - UFMG
Leonardo Torres, Department of Electronics Engineering - Federal University of Minas Gerais - UFMG
Leonardo Mozelli, Department of Electronics Engineering - Federal University of Minas Gerais - UFMG
Motivated by the seminal paper published by Luis Pecora and Thomas Carroll in the early nineties, the secure communication
based on chaotic systems synchronization has become a subject of increasing interest in the scientific community. While
much has been accomplished in realm of theory, much less has been reported in terms of practical results. Certainly, one of
the reasons of this could be the difficulty to assembly a suitable practical setup for testing new theoretical ideas as
opposed to just simulating solutions on a digital computer.
In this work, a systematic project methodology is developed to deal with the chaotic synchronization of Lur'e systems in a
discrete-time domain. The theory developed here is applied in a laboratory setup that implements a secure communication
experiment. The secure communication is accomplished based on the information transmission through a synchronization control
principle applied to coupled nonlinear Chua oscillator circuits.
The project methodology proposed is derived from a concatenation of some important ideas recently published in the
literature concerning nonlinear systems. The project steps consist in system identification and parameter estimation,
discretization, state-observer concepts and application of robust control techniques based on Linear Matrix Inequalities -
LMIs. In the context of secure communication, the performance index H-infinity norm appears as a criterium that improves
the information protection and ensures a better information reconstruction.
Even though the theoretical results presented in this paper are correct for all possible scenarios, there are practical
issues that should be addressed. In this work, issues such as increasing the value of the frequency of the information
signal to be transmitted are shown to be different from the expected theoretical (simulation) results.
42.Reproduction Of Chaotic Systems Using Analogue Electronic Circuits
Ronilson Rocha, Dept of Control and Automation, Federal University of Ouro Preto - DECAT/EM/UFOP, rocha@em.ufop.br
Luiz S. Martins-Filho, Dept of Computer Science, Federal University of Ouro Preto - DECOM/ICEB/UFOP
Romuel F. Machado, Dept of Physics, Federal University of Ouro Preto - DEFIS/ICEB/UFOP
Ricardo Sergio Prado, Federal Center of Technological Education of Ouro Preto - CEFET-OP
Numerous natural and artificial systems are completely described by deterministic dynamic laws and nonlinear differential
equations without stochastic components, but present an unpredictable and apparently random dynamical behavior extremely
sensitive to initial conditions. They are known as Chaotic Systems, and have been studied by mathematicians, physicians,
engineers and, more recently, specialists in information and social sciences. Several properties of chaotic systems as
controllability and sometimes self-synchronization assure various types of applications with a great potential commercial
and industrial in several areas, such as Engineering, Computers, Communications, Medicine and Biology, Management and
Finance, Consumer Electronics, Information Processing, etc. Experimental activities involving chaotic systems play a very
important role to understand theoretical concepts and encourage the confrontation with practical challenges. However, the
implementation of an experimental laboratory meets several challenges, such as space limitations, financial support,
difficulties to build a real system, etc. In this context, the concept of electronic analogy can be extremely helpful in
developing experimental activities. Since any dynamical system can be expressed by differential equations, its dynamical
behavior can be mimicking from analogous electronic circuits assembled with robust, compact, inexpensive and versatile
electronic components easily found in market. In this analogy, the original system variables and its derivatives are
represented by electric signals, and the system behavior can be directly observed and recorded on oscilloscopes and/or
acquisition boards, avoiding the use of expensive and complex sensor devices. Although an electronic prototype does not
reproduce completely the real system, it allows an experimental and qualitative study of its dynamical behavior, incorporating
several aspects of practical implementations such as unpredictable noises, uncertainties, measurement problems and failures.
Another advantage of electronic analogy is the possibility of on-line adjustments on system parameters. However, since
electric signals are generally subjects to hard limitations, to assure a correct operation and the integrity of the
electronic devices, a correct reproduction of a dynamical system from a direct electronic implementation can become
relatively difficult. This work presents a methodology to design analogous electronic circuits that reproduce the dynamical
behavior of physical systems. The implementation of these electronic circuits can be used in practical experiments for the
study of dynamical systems and other related subjects. It is always desirable to obtain an electronic version of any system
as simple as possible to reduce difficulties on its implementation. If necessary, the original model must be modified to
restrict the amplitudes and frequencies of electrical signals aiming to respect the limitations imposed by electronic
devices and to assure a correct reproduction of dynamical system. A study of cases is presented, where electronic circuits
are designed and experimentally implemented to reproduce the dynamical behavior of four known chaotic systems: forced
Duffing system, Lorenz system, Rössler system and Chua system.
43.Improving Taylor’s Analogue Predictor For Broadband Chaotic Signals
Arunas Tamasevicius, Plasma Phenomena and Chaos Lab., Semiconductor Physics Institute, tamasev@pfi.lt
Mantas Meskauskas, Plasma Phenomena and Chaos Lab., Semiconductor Physics Institute
Gytis Mykolaitis, Plasma Phenomena and Chaos Lab., Semiconductor Physics Institute
Recently we described an extremely simple analogue circuit for prediction of time-continuous signals on a real time scale
[1,2]. The performance of the predictor was demonstrated both experimentally [1] and numerically [2] using narrowband
periodic and broadband chaotic signals. The predictor is convenient for short-term predictions, especially when the system
model is not available. However the developed experimental prototypes using active RC filters exhibit noticeable
distortions of the predicted signals. The point is that the circuit includes finite number of the first-order RC filters,
i.e. it actually implements Taylor’s series expansion with a finite number of terms. The transfer function is characterized
by rather strong frequency dispersion [2]. Therefore the predictor is less suitable for broadband signals, like chaotic
waveforms. In the present paper we suggest to supplement the low-order Taylor’s predictor with the Lagrange remainder.
Practical implementation of the improved predictor requires insertion of adequate delay unit(s). The modified circuit is
described in details and is investigated experimentally using chaotic waveforms from electronic oscillator [3]. The
prediction errors are measured.
This research was supported by Lithuanian State Science and Studies Foundation.
[1] M. Meskauskas, A. Tamasevicius, K. Pyragas, G. Mykolaitis, Proc. Int. Symp. NOLTA2005, October 18-21, Bruges, Belgium,
p.385 (2005).
[2] M. Meskauskas, A. Tamasevicius, K. Pyragas, Int. J. Bifurcation and Chaos (2006).
[3] A. Tamasevicius, G. Mykolaitis, V. Pyragas, K. Pyragas, Eur. J. Phys. 26, p.61 (2005).
44.Chaos And Pattern Formation In A Food Chain Of Two And Three Species
Sabrina Araújo, IFGW-UNICAMP, salino@ifi.unicamp.br
Marcus Aloízio Martinez de Aguiar, IFGW-UNICAMP
We study the dynamics of ecological populations of predators and preys using two different approaches. The first is a Mean
Field approach, where we assume that the individuals are homogeneously mixed in space, so that they interact with one
another with equal probability and space is not explicitly treated. The second approach, on the other hand, considers that
the individuals of each species are distributed in space, where they can migrate and interact only with those that are in a
given neighborhood around their position. In both models we consider discrete time and, in case of spatial model, discrete
space as well.
We study the dynamics generated by the interaction of two species, a predator and a prey, and also the dynamics of a system
with three species, utilizing both models. The mean field model shows the appearance of several types of attractors,
including chaotic ones. In the spatial model we emphasize that the size of the interacting neighborhood modifies the
dynamics and the organization of the species in the space. When the interacting neighborhood has intermediate values
super-populations arise. However, if we increase this interacting neighborhood, the super-populations vanish and the
spatial model recovers mean field model. We also observe situations where the population oscillations become synchronized
during the time evolution.
45.A Global Model From The Canadian Lynx Cycles As A Proof Of Chaos In Ecosystems
Jean MAQUET, CORIA UMR6614 - Université et INSA de Rouen, Jean.Maquet@insa-rouen.fr
Many ecological and biological populations oscillates with the remarkable property that their period length is quite
constant while their abundance levels have large amplitude fluctuations [1,2].
Among the rare data available, there are the cycle in populations of Lynx canadensis which has received wide attention on
account the great amplitude of the rhythm it has produced in the fur catches of the Hudson’s Bay Company over a long period.
According to Elton and Nicholson’s conclusions [3], the fluctuations of the Lynx are related to those of the snowshoe rabbit
(Lepus americanus) and aquatic species such as the muskrat (Ondatra Zibethica). This is therefore an ecosystem involving at
least three species and chaotic behaviors are thus expected as observed in many three species models (see [4, 5, 6] among
others).
Unfortunately, all the models proposed are empirical, that is, the models are searched to reproduced “chaotic” fluctuations
which look like the observations. Indeed, almost all data available have few cycles which constitutes a too small data set
to directly identify a chaotic attractor. One of the very interesting method to avoid such difficulty consists in getting
a global model from the data. Indeed, from a very limited number of cycles, it is possible to extract a global model — a
set of three ordinary differential equations directly estimated from the data without any constraint on the model
structure — which reproduces the main features of the dynamics [7, 8]. It will be shown that a 3D model can be estimated
from the Canadian lynx furs caught (1821-1937) as reported by Elton and Nicholson [3]. Using a topological analysis, the
chaotic attractor is found to be topologically equivalent to the attractor solution to a standard three level food chain
proposed by Blasius et al [6] as a good candidate for explaining the irregular fluctuations in the Lynx populations. To our
knowledge, this could be one of the very first proof of chaos in ecosystems.
References
[1] W. S. C. Gurney, S. P. Blythe & R. M. Nisbet, Nicholson’s blowflies revisited, Nature,287, 17-21, 1980.
[2] W. M. Schaffer, Stretching and folding in lynx fur returns: evidence for a strange attractor in nature ?, The American
Naturalist, 124, 798-820, 1984.
[3] C. Elton & M. Nicholson, The ten-year cycle in numbers of the Lynx in Canada, Journal of Animal Ecology, 11, 215-244,
1942.
[4] M. Gilpin, Spiral chaos in a predator prey model, The American Naturalist, 113, 306-308, 1979.
[5] R. K. Upadhyay, S. R. K. Jyengar & V. Rai, Chaos : an ecological reality ?, International Journal of Bifurcation &
Chaos, 8 (6), 1325-1333, 1998.
[6] B. Blasius, A. Huppert & L. Stone, Complex dynamics and phase synchronization in spatially extended ecological systems,
Nature, 399, 354-359, 1999.
[7] G. Gouesbet & J. Maquet, Construction of phenomenological models from numerical scalar time series, Physica D, 58,
202-215, 1992.
[8] C. Letellier, J. Maquet, L. A. Aguirre & R. Gilmore, An equivariant 3D model for the long-term behavior of the solar
activity, 7th Experimental Chaos Conference, San Diego, 25-29 Aout 2002, Ed. Visarath In, AIP Press, March 2003.
46.An Introduction To The Juridical System, Private Law And Chaos
Ricardo Aronne, PUCRS, aronne_ricardo@hotmail.com
An Introduction to the Juridical System, Private Law and Chaos
Summary Prisms of a Research on Civil-constitutional Law
47.Weighting Coefficients Versus Constraints In Nonlinear Dynamics
Feruccio Bilich, University of Brasilia - UnB, bilich@unb.br
Ricardo DaSilva, CNPq
In this work is presented the weighting coefficients method which consists in encoding directly into the objective
function information which is usually encoded in the form of constraints. This procedure is especially helpful in nonlinear
modelling and nonlinear dynamics.
It is explained the advantages of the use of weighting coefficients in contraposition to the disadvantages of the use of
constraints in mathematical programming. It is shown how some special cases of objective functions such as multinomial
distribution (discrete functions) and gamma and exponential distributions (continuous functions) with constraints can be
represented by an equivalent function with weighting coefficients.
Finally a general proof of the weighting coefficients method is derived.
48.Fermi-Ulam Models: Scaling Properties On Variables Time And Interactions Number
Denis Gouvêa Ladeira, Universidade Federal de Minas Gerais, dgl@fisica.ufmg.br
Jafferson Kamphorst Leal da Silva, Universidade Federal de Minas Gerais
The Fermi-Ulam accelerator model consists of a ball confined between a rigid fixed wall and an oscillatory moving one. The
ball collides elastically with the walls and the system can be described by an area preserving map. In high energies regime
the phase space presents KAM islands surrounded by locally chaotic regions, which are limited by spanning curves. Below the
invariant spanning curve of lower energy a globally chaotic sea involves KAM islands. The presence of invariant spanning
curves limits the orbits in phase space impeding unlimited energy growth (Fermi acceleration). The simplified Fermi-Ulam
model (SFUM) consists of an approximation in which the oscillating wall keeps a fixed position, but transfers energy and
momentum to the particle at each collision as if it was moving. This simplification speeds up the simulations substantially
as compared with the full model and the phase space of SFUM presents basically the same structure of FUM.
If the oscillation amplitude of the moving wall is zero the system is integrable but as soon as this amplitude is different
from zero the FUM behaves chaotically. Near the transition integrable-chaotic, average quantities can be described by
scaling functions [1, 2].
In this work we are interested in the chaotic sea below of the spanning curve of lower energy for FUM and SFUM. We study
scaling properties of average energies on variables time, t, and interactions (or collisions) number, n. By construction,
one interaction of the map gives the velocity of the particle and the phase of the moving wall after one collision and,
therefore, average quantities can be evaluated without problems on variable n. Although less direct, we can determinate
averages quantities on variable t by comparing the time intervals between a given instant and: (1) the next collision
instant and (2) the instant of the next measurement of interest. Numerical analysis on variable t shows that the average
energy of SFUM presents a slow (power-law) decay for large times, in contrast with FUM, in which the average energy reaches
a stationary value for t?8. In SFUM successive collisions with the moving wall do not occur, and, therefore, when the
particle has very low velocity, it remains with low energy for a long time, originating the decay in energy for large
values of t. Moreover, we show that if t is employed as independent variable, then the exponents related to the scaling
properties of FUM and SFUM are not the same. However, if n is employed as independent variable, then both FUM and its
simplification present the same set of exponents.
References:
[1] E. D. Leonel, P. V. E. McClintock and J. K. L. da Silva, Phys. Rev. Lett. 93, 14101 (2004).
[2] D. G. Ladeira and J. K. L. da Silva, Phys. Rev. E 73, 026201 (2006).
49.Nonlinear Resonance Of KAM Tori In Bouncing Universes
Ivano Damiao Soares, Centro Brasileiro de Pesquisas Fisicas - CBPF/MCT, ivano@cbpf.br
Henrique Pereira de Oliveira, Departamento de Fisica Teorica - UERJ - RJ
Eduardo Valentino Tonini, Centro Federal de Educacao Tecnologica - CEFETES - ES
A class of two-dimensional Hamiltonians is studied where nonlinear resonance of KAM tori take place. The Hamiltonian may
describe the dynamics of closed Friedmann-Robertson-Walker universes with a massive inflaton field where Friedmann
equations are corrected by the introduction of a potential term that implements nonsingular bounces in the early evolution
of the universe. This potential term arises from quantum gravity/high energy corrections to cosmological scenarios near the
singularity and is semiclassical in nature, being effective only when the scale factor is very small (the Hamiltonian may
also approximate the dynamics of coupled vibrational modes of triatomic molecules). For certain windows in the parameter
space, labeled by the scalar field mass and the conserved Hamiltonian, phenomena of nonlinear resonance show up. Nonlinear
resonance may induce the destruction of KAM tori that trap the inflaton, leading to a rapid growth of the scale factor and
the scalar field, with disruption of metastable states and consequent escape of the universe into inflation. We make a
numerical/analytical approach to the nonlinear resonance phenomena, characterizing a particular resonance by its
characteristic periodic orbits and by the structure of the associated diffusion pattern. The diffusion occurs when the
orbit escapes through a Cantorus in the border of primary KAM islands that encloses the characteristic periodic orbits of
the resonance. The windows of parametric resonance, characterized by an integer $n \geq 2$ (associated with the ratio of
the frequencies in the scale factor/scalar field degrees of freedom) are the ones that strongly favor inflation in the
system. We discuss how generic is this behavior for inflationary models, and its possible consequences for structure
formation.
50.A Hybrid Chaotic Dynamic And Evolutionary Computation Approach For Load Forecasting
Clodomiro Unsihuay, UNIFEI, unsihuay@ieee.org
A. C. Zambroni de Souza, UNIFEI
J. W. Marangon Lima, UNIFEI
Accurate forecasting of electricity demand is essential for successful participation in deregulated retail electricity
markets. Energy service providers require the information to plan long-term power supplies, estimate end user service
costs, price retail service, plan short-term delivery schedules, assess market risk exposure, and ultimately determine
the sources of imbalance charges due to forecast errors. The new dynamics of electricity markets, i.e. the high price
volatility and a noticeable amount of short-term an long-term contracting, would influencing in electricity load times
series dynamics, became a non-stationary time series typically produced by a dynamic system with chaotic behavior, or not
completely stochastic behavior, etc. Thus, to develop methodology to capture complicated electricity load dynamics or
characteristics became vital.
In recent years chaos time series analysis has been studied to investigate complicated nonlinear dynamical systems. A model
with deterministic chaos can be expressed in a deterministic rather than stochastic model if a given time series is a
chaotic one. It happens that given complicated systems seem to be stochastic from micro point of view while they correspond
to deterministic systems from macro point of view and that some complicated time series correspond to deterministic chaos.
A novel hybrid nonlinear chaotic dynamic and evolutionary strategy based model for short-term load forecasting and
long-term peak-load forecasting. The proposed model to insert a new stage named in this work as training stage into of a
nonlinear chaotic dynamic based predictor. Therefore, improving time series modeling and forecasting. This novel training
stage is done through evolutionary strategy. This training stage is done such as five optimal parameters for a nonlinear
chaotic dynamic based predictor are found. In other words an optimal time series identification stage is developed to
identify a model with good prediction capabilities. Hence, a common identification objective is to minimize the mismatch
between model prediction and observed data. Hence also, the parameters of nonlinear chaotic dynamic based predictor have
constraints. Thus, in this paper, an evolutionary strategy optimization (ESO) algorithm is developed to effectively handle
this identification problem, thus improving the prediction of a nonlinear chaotic dynamic based predictor.
ESO uses human evaluation in the optimization system. Simply stated, ESO is a technique from the class of evolutionary
algorithms (EAs), which are based upon a simple model of organic whose fitness function is replaced by a human. As in
interactive evolution, the user selects one or more individual(s) which survive(s) and reproduce(s) (with variation or
mutation) to constitute a new generation.
Test results shown that, the proposed model effectively capture the time series dynamics indifferent of type (stochastic,
chaotic, etc) or combination (stochastic-chaotic, etc) of dynamics of times series. The proposed approach has been
implemented in MATLAB, named in this paper as PREDICT2-ESO.
The proposed model is applied for a Brazilian e a North-American electric utility. It is required to predict short term
hourly load and either short term and long peak-load during the next two years. The proposed model is compared with ARIMA
model. The results are promising; a comparative analysis suggests that a proposed model outperforms those others models
considered in this work.
51.Chaos And Anomalous Transport In A Unidimensional Lattice Of Coupled Kicked Rotors
Cristiano Francisco Woellner, Universidade Federal do Paraná, cfw00@fisica.ufpr.br
Ricardo Luiz Viana, Universidade Federal do Paraná
Sergio Roberto Lopes, Universidade Federal do Paraná
We study some dynamical aspects of a unidimensional lattice of kicked rotors using a Hamiltonian coupled map lattice with
a coupling strength which decreases with the lattice distance as a power-law. We investigate concepts as stickness,
Lyapunov exponents , KS-entropy and transport in the phase space. In the study of these Hamiltonian systems it is important
to understand how these systems approach the equilibrium state. Moreover we investigate the effect of the stickness changes
as the system approaches the equilibrium state as well as the anomalous diffusion in the momentum space.
52.Transition To Intermittent Chaotic Synchronization
Liang Zhao, Institute of Mathematics and Computer Science, University of São Paulo, zhao@icmc.usp.br
Ying-Cheng Lai, Arizona State University
Coupled chaotic oscillators can exhibit intermittent synchronization in the weakly coupling regime, as characterized by the
entrainment of their dynamical variables in random time intervals of finite duration. We find that the transition to
intermittent synchronization can be characteristically distinct for geometrically different chaotic attractors. In
particular, for coupled phase-coherent chaotic attractors such as those from the Rössler system, the transition occurs
immediately as the coupling is increased from zero. For phase-incoherent chaotic attractors as those in the Lorenz system,
the transition occurs only when the coupling is sufficiently strong. A theory based on the behavior of the Lyapunov
exponents and unstable periodic orbits is developed to understand these distinct transitions.
53.Control Of Drift Wave In The Plasma Edge Tokamak
Antonio Marcos Batista, Departamento de Matematica (UEPG), batista@interponta.com.br
Ibere Luiz Caldas, Instituto de Fisica (USP)
Ricardo Luiz Viana, Departamento de Fisica (UFPR)
Sergio Roberto Lopes, Departamento de Fisica (UFPR)
Drift waves typically occur in magnetized and inhomogeneous plasmas, and provide a mechanism for energy and particle
transport across magnetic field lines. In the magnetically confined plasma in tokamaks, for example, there are strong
density and temperature gradients at the plasma edge. Assuming the main tokamak magnetic field as lying in toroidal
direction, and the density gradients along the radial direction, there appears a diamagnetic plasma current along the
poloidal direction. Due to the long-range charged particle interaction, there appears a drift-wave poloidal electric field,
perpendicular to the magnetic field, which produces drifts of the gyro-motion in the radial direction, i.e. across magnetic
field lines. We use a description for drift-wave propagation via Hasegawa-Mima equation, analyzing a Fourier mode
decomposition which retains three interaction modes, with a fourth and resonant wave controlling chaotic evolution of the
three-wave system.We have only considered the time evolution of the Fourier modes of the drift-wave potential.This means
that our observations hold only for fixed spatial positions, which is consistent with the fact that measurements are made
using probes at such positions.
54.Wavelet Analsis Of Chaotic Oscillations In A Steady State Glow Discharge Plasma
Sekar A.N. Iyengar, Saha Institute of Nuclear Physics, ansekar.iyengar@saha.ac.in
Chaotic Ocillations have been observed in a d.c. glow discharge plasma as a function of the applied discharge voltage and
neutral pressure. These oscillations exhibit a highly nonlinear relaxation type of oscillations with atleast seven to eight
distinct frequencies at higher voltages and goes into an almost sinusoidal oscillation through period subtraction as
voltage is decreased. What is different from the traditional analysis is that we have carried out a wavelet analysis of
these oscillations which bring out certain new features that are missing in the traditional fourier analysis. Phase Space
plots of these oscillations are also presented . Modifications of these oscillations in the presence of dust particles
(dusty plasma ) will also be presented.
55.Chaotic Magnetic Field Lines For Shearless Tokamaks
Tiago Kroetz, Departamento de Física, ITA, kroetzfisica@yahoo.com.br
Marisa Roberto, Departamento de Física, ITA
Elton C. Silva, Instituto de Física , USP
Ibere L. Caldas, Instituto de Física, USP
Ricardo Viana, Departamento de Física, UFPR
Shearless as well as negative magnetic shear configurations in tokamaks reduce substantially particle diffusivity and
improve plasma confinement. There are some advantages of producing discharges with reversed magnetic shear such as: a high
fraction of the self-sustained bootstrap current aligned with the current density profile and a reduction of the plasma
transport in the central region of the plasma column, through the formation of a transport barrier, or a region where both
the electron and ion diffusivities are greatly reduced around the shearless region. In this work we use an analytical
approach by considering a convenient coordinate system in which the Grad-Shafranov equation can be analytically solved in
an approximated way. A toroidal current density profile with a central hole was considered in order to create a shearless
safety factor profile. We introduce a Hamiltonian description for the field lines, in terms of action and angle variables,
to determine the safety radial profile of the magnetic surfaces. The effects of an ergodic magnetic limiter (EML) on the
magnetic field line structure were investigated. The main result is the creation of an outer chaotic layer which traps the
field lines. The topology of the field lines and the reconnection and bifurcation phenomenon were studied by using Poincarè
maps.
56.Spectral Analysis Of The TCABR Turbulence
Gustavo Zampier dos Santos Lima, USP, gustavo_zampier@yahoo.com.br
Zwinglio O. Guimaraes Filho, USP
Ibere L. Caldas, USP
Maria Vittoria A. P. Heller, USP
Improvement of plasma confinement in tokamaks depends on plasma edge behavior. Experiments indicate that this behavior
depends on the anomalous particle transport caused by the electrostatic turbulence. Thus, it is important to study this
turbulence and its control. To investigate this turbulence at the TCABR tokamak, we analyze magnetic and electrostatic ?
uctuations obtained from experimental data measured by a set of Langmuir probes and magnetic coils. These fluctuations have
been measured in discharges modified by an external perturbation due a DC biased electrode1. As shown in Ref.[1], this
perturbation, applied during the discharges, modifies the ?uctuations. To investigate these non-stationary fluctuations, we
apply Fourier and wavelet spectral analyses to describe their spectral properties and how these properties change in time.
By decomposing the experimental time series into time-frequency space, we determine both the dominant modes and how these
modes vary in time. To obtain the discrete wavelet transform, we choose the Morlet wavelet consisting of a plane wave
modulated by a Gaussian. A distinctive peculiarity, caused by the electrode perturbation, in some of the analyzed discharges
is the modulation of electrostatic turbulence by the magnetic oscillations shown by the similar frequency power spectra of
these two oscillations1. Moreover, the auto-correlation analysis of the electrostatic turbulence oscillates with the
magnetic oscillation frequency ( 10kHz) with long term ( 0.5ms) and high correlation (amplitude of 0.6) coeficients,
confirming the reported modulation. [1]. I. C. Nascimento, Y. K. Kuznetsov, J. H. F. Severo, A. M. M. Fonseca, A. El?mov,
V. Bellintani, M. Machida, M. V. A. P. Heller, R. M. O. Galvao, E. K. Sanada, J. I. Elizondo, Nuclear Fusion 45, 796 (2005).
57.The Dynamics Of Pattern Formation In A Complex System
Robson Luiz Santos, UFMG, robson@fisica.ufmg.br
Ubirajara Agero Batista, UFMG
José Marcos Andrade Figueiredo, UFMG
A macroscopic system existing in a nonequilibrium thermodynamic state may present a low entropy branch. In this case, the
subjacent non-linear effects that appear can originate self-organized structures presenting spatio-temporal patterns. In
this work, we present studies on the dynamics of a pattern formed in a fluid-fluid interface after a supercritical
pitchfork bifurcation. We were able to measure the growth rate of pattern modes which indicate that an exponential trend
drives the onset of the development of the pattern. Our data fits well to growth rate values obtained from the linear
stability analysis appropriated for this system. After this exponential trend, the pattern time-evolution shows amplitude
saturation of the modes. The whole amplitude curve fits well to a Ginzburg-Landau equation, even for states far away from
the bifurcation point, where curvature effects present in the pattern becomes relevant.
We were also able to perturb the highly symmetric branch, before the bifurcation point is reached, and see how it is
affected. Oscillatory modes in the planar interface were observed, indicating the existence of a precursor anticipating the
bifurcation. Careful studies of the observed precursor modes indicate the existence of critical amplification of the modes
and defines a new "precursor branch" not predicted by the linear stability analysis. Given that the perturbation we
imposed on the system possess a specific time-dependence, the observed precursors can be classified as "deterministic" and
differ from the others reported up to now in other systems, which come mainly from a noisy perturbation. However, the
amplitude of the precursor modes we measured fits well to a class of power law which may indicate that a universality class
for this phenomenon may exist.
58.Chaotic Transport In Tokamaks
F. Alberto Marcus, IFUSP, albertus@if.usp.br
I.L. Caldas, IFUSP
Electrostatic fluctuations induce the anomalous particle transport observed at tokamak plasma edge. It is important to
estimate the importance of chaotic particle orbits on this transport. For large aspect-ratio tokamaks, these fluctuations
can be approximately described by a superposition of many toroidal and poloidal drift waves that are described by an almost
integrable hamiltonian formalism. The ions guiding center transport caused by these waves can be estimated by the
lagrangian chaotic transport in the particle phase space. The drift produced by the radial electric field is represented by
the integrable part of the Hamiltonian, while the other part contains periodic perturbations representing the fluctuations
of the electric field associated to the drift waves. In this work, we study the resonances and islands chains created on
the phase space due to the superposition of two dominant drift waves described by two diferents Hamiltonian models. In
these models the chosen stream function describe drift waves concentrated at the plasma edge or covering all over the
plasma. Thus, for experimental parameters usually observed in tokamaks, we analyze bifurcations and the onset of chaos in
this system.
59.Multifractal Spectra in a Faraday experiments
Rosen Marta, Professor, mrosen@fi.uba.ar
Maria Piacquadio, Professor
Cecilia Cabeza, Professor
Between the acceleration/frequency threshold after which the classical Faraday patterns appear, and the new threshold
corresponding to the ejection of droplets (spray), there is an intermediate zone with a structure which is the object of
our study. This intermediate state is characterised by the formation of “cusps” on the surface of the fluid under study;
the behaviour of the geometrical patterns formed by these “cusps” depends on the control parameters of the system.
The Faraday experiment consists of a layer of fluid in a horizontal cell submitted to a periodic vertical force, its
frequency and acceleration being the control parameters. The behaviour of the “cusps” is studied with the aid of a pair of
electrodes between which there is a voltage difference. One of the electrodes is submerged in the liquid; the other is
suspended over the fluid surface at a controllable distance. When a cusp rises and touches the electrode above, it closes a
circuit and a current is generated yielding a signal, electronically detected and processed.
The signal is analysed by considering the system response as drawing a Cantor-dust fractal set, cusp-touching-electrode
being a point of the fractal. Our aim is to compare the different multifractal spectra for the Cantor dusts corresponding
to different accelerations for a fixed frequency. In each case, a sample of 10,000 points distributed in 100 boxes of equal
size were considered (these values were deemed adequate for the conditions of our experiment) in order to obtain the
corresponding spectra with the same multifractal parameters. The evolution of the spectrum, as the acceleration increases,
permits detecting and determining the so-called "crisis" threshold, beyond which a qualitative change in the physics of the
system takes place.
60.Escape Pattern And Transport Barrier In Shearless Tokamaks
Marisa Roberto, Departamento de Física, ITA, marisar@ita.br
Elton C. Silva, Instituto de Física, USP
Ibere L. Caldas, Instituto de Física , USP
Ricardo Viana, Departamento de Física, UFPR
In order to investigate the field lines exit basins in tokamaks, external resonant fields created by an ergodic magnetic
limiter were considered. The exit basins are a set of points in the chaotic region which originates field lines hitting the
wall in some specific region. They have a fractal geometry structure, so that the field line collisions with the tokamak
wall do not yield uniform patterns, but a fractal distribution of spots on the wall named magnetic footprints. In this work
we investigate the exit basins and the magnetic footprints using a non-monotonic safety factor profile, for which there is
a region of negative magnetic shear as well as a shearless radius. The nontwist mapping were obtained for some values of
the ergodic limiter current which describe perturbed magnetic field lines with two chains of magnetic islands and chaotic
lines in their vicinity. The observed escape pattern changes with the perturbation intensity. There is an extremely
concentrated escape in the tokamak wall nearby the equatorial region, if internal modes are perturbed. On the other hand if
modes near the tokamak wall are perturbed the escape channels are more distributed. The magnetic footprints are shown as a
function of poloidal angle.
61.Experimental Synchronous Competing Plasma Oscillators
Epaminondas Rosa, Illinois State University, erosa@ilstu.edu
There is a multitude of examples where coupled systems compete to get into a synchronous state with a particular
oscillator. Think, for instance, of two neurons in the brain competing to get the attention of a third neuron, and
eventually developing some sort of synchronous process. This is not an infrequent feature involving three or more
mutually coupled oscillators, and can be studied both experimentally and numerically. In this talk, experimental results
obtained from plasma discharges coupled to periodic and chaotic oscillators will be presented showing peculiarities related
to the types of oscillators and to the types of couplings. In particular, in the case of two oscillators competing for
synchronization with a third oscillator, the target oscillator synchronizes alternatively to one or the other of the
competing ones. The time intervals of synchronous states vary in a random-like manner. Numerical simulation results show
consistency with experimental data.
62.Noise-Driven Alfvén Intermittency In Space And Laboratory
Wanderson Santana (1), INPE, wanderson@dge.inpe.br
A. C.-L. Chian (1), INPE
E. L. Rempel (2), ITA
(1) National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515,
São José dos Campos-SP, 12227-010, Brazil (wanderson@dge.inpe.br / Phone: +55-12-3945-6839)
(2) Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), CTA/ITA/IEFM,
São José dos Campos-SP, 12228-900, Brazil
Chaos theory provides powerful tools for the study of space and laboratory plasmas (Chian et al., 1998; Rempel and Chian,
2005). For example, Chian et al. (2002) characterized the destruction of attractors in a nonlinear Alfvén wave system,
where up to four different attractors coexist. In this work, the role of noise in the generation of transient and
intermittent behaviors in Alfvén waves modeled by the derivative nonlinear Schrödinger (DNLS) equation is investigated.
The study of intermittency is crucial for the understanding of physical processes underlying the Alfvén wave propagation in
space and laboratory plasmas, e.g., plasma heating and particle acceleration in solar corona and the Earth´s aurorae, as
well as tokamak experiments. By using chaos approach, it is shown that the Alfvén intermittency can be seen as a dynamical
phenomenon, where the action of external noise triggers the hopping between different coexisting attractors (Rempel et al.,
2006). The role of nonattracting chaotic sets known as chaotic saddles (Rempel et al., 2004) in the hopping dynamics is
discussed. Since noise sources are always present in space and laboratory plasmas, it is plausible that the intermittent
phenomena observed in real plasma data are in fact a signature of multistable regimes in the presence of noise.
References:
[1]Chian, a. C.-L., F. A. Borotto, and W. D. Gonzalez (1998). Alfvén intermittent turbulence driven by temporal chaos,
Astrophysical Journal, 505, 993.
[2]Chian, A. C.-L., F. A. Borotto, and E. L. Rempel (2002), Alfvén boundary crisis, International Journal Bifurcation and
Chaos, 12, 1653.
[3]Rempel, E. L., A. C.-L. Chian, E. E. N. Macau, and R. R. Rosa (2004), Analysis of chaotic saddles in low-dimensional
dynamical systems: the derivative nonlinear Schrödinger equation, Physica D, 199, 407.
[4]Rempel, E. L., and A. C.-L. Chian (2005), Space Plasma Dynamics: Alfvén intermittent chaos, Advances in Space Research,
35, 951.
[5]Rempel, E. L., W. M. Santana, and A. C.-L. Chian (2006), Alfvén multistability: transient and intermittent dynamics
induced by noise, Physics of Plasmas, in press.
63.Are The Porous Silicon Structures Chaotic?
Mariana Baroni, LAC-INPE, mariana@lac.inpe.br
R R Rosa, LAC-INPE
J Pontes, COPPE-UFRJ
In this work it is developed implementation of different nonlinear models that describe processes of growth and its
corresponding universality class: (i) ballistic deposition; (ii) random deposition; and (iii) KPZ. Due to its physical
properties, the KPZ 2D is adopted to simulate the structure of porous materials with spatial characteristics equivalents
those finding in porous silicon samples. The analysis of the modeling was done using both scaling concepts and application
of the Gradient Pattern Analysis in the results gotten from the models as in the experimental AFM (Atomic Force Microscopy)
images of the samples of porous silicon. A classification of global and local nonlinear structural patterns is considered
discussing its importance for the area of complex nonostructured porous materials. The growth exponent of irregular
spatio-temporal temporal structures found from the numerical simulations are presented in the context of a possible
signature of spatio-temporal chaos into the dynamical process for porous silicon experimental samples generation.
64.Classical Magnetoresistance Of Two-Dimensional Electrons Constrained To Non-Planar Surfaces And Antidot Potentials
Nilo Mauricio Sotomayor, Universidade Federal do Tocantins, nmsch@uft.edu.br
J. F. da Rocha Neto, Universidade Federal do Tocantins (Arraias)
G. M. Gusev, Instituto de Física da Universidade de São Paulo
The advent of epitaxial regrowth techniques, has recently leaded to the obtention of a two-dimensional electron gas (2DEG)
constrained to non-planar topographies [1]. The electron transport in these systems is influenced by a complex chaotic
dynamics, that develops, under the influence of a spatially fluctuating magnetic field and random antidot potentials.
Magnetotransport measurements at liquid helium temperatures show a variety of new phenomena such us, anomalous Hall effect,
negative magnetoresistance, commensurability oscillations, large linear decrease of magnetoresistance and, damping of the
Shubnikov-de Haas oscillations. Most of these phenomena, that occur, at low magnetic field values, in high mobility samples, are in disagreement with the conventional Drude-Boltzmann approach for magnetoresistance and, remains still not well understood. In the present work, we present the results of numerical calculation of the magnetoresistance for a two-dimensional electron gas in a lattice of antidots and constrained to move in non-planar topographies. As for experimental samples, the length of the Fermi wave-package is smaller than the period of the magnetic field modulation and also than the antidote lattice period, we used classical theory, based on a Hamilton-Dirac method for constrained systems together with linear response[2] for the calculation of the electron trajectories and longitudinal and transversal resistivities. We calculated magnetoresistance when the magnetic field vector is along the direction, that is, perpendicular to the corrugated surface, and also when the magnetic field is tilted to the plane of the surface. The cases of non-uniform magnetic field with zero mean and without zero mean were treated. For
both cases we found that, when the magnetic field vector is perpendicular to the surface, and the diameter of the antidot
potential at the Fermi energy is small, magnetoresistance displays commensurability oscillations periodic with the inverse
of the magnetic field. As the electron motion is only sensitive to the normal component of the magnetic field to the
surface, a drift of the guiding center is created by the small gradient of the magnetic field modifying the transport
properties of the 2DEG. When the magnetic field vector is tilted away from the perpendicular direction, towards the
parallel direction , the commensurability peaks shift steadily to higher values of the field, and when the magnetic field
is parallel to the corrugated surface a single peak is observed together with positive magnetoresistance.
References:
[1] G. M. gusev, A. A. Quivy, J. R. Leite, A. A. Bykov, N. T. Moshegov, V. M. Kudryashev, A. I. Toropov, and Yu. V.
Nastaushev, Semicond. Sci. Technol. 14, 1-5 (1999).
[2] N. M. Sotomayor, J. F. da Rocha Neto, and G. M. Gusev, accepted to be published at Brazilian Journal of Physics (2006).
65.High Frequency Synchronization In A Network Of Inhibitory Interneurons: Dependence On The Biophysical Properties Of The
Neural Model
Santi Chillemi, CNR - Istituto di Biofisica, santi.chillemi@pi.ibf.cnr.it
Angelo Di Garbo, CNR - Istituto di Biofisica
Santi Chillemi, Angelo Di Garbo CNR – Istituto di Biofisica Via G. Moruzzi 1, 56124-Pisa, Italia chillemi@pi.ibf.cnr.it,
digarbo@pi.ibf.cnr.it http://www.pi.ibf.cnr.it/
Experimental findings revealed that pyramidal neurons codifying for the different features of a visual stimulus synchronize
their firing activities in the gamma frequency band (30–80 Hz) [1]. Both experimental and theoretical investigations suggest
that a population of coupled inhibitory interneurons generates synchronous firing regimes and modulates the firing activity
of pyramidal cells [2-13]. Moreover, recent experimental results show that interneurons are interconnected by electrical
synapses too [4, 5]. Thus an important problem is to understand the mechanisms leading to the emergence of synchronous
firing in a network of interneurons coupled by inhibitory and electrical synapses. Increasing the discharge frequency of
the cells was shown to promotes the synchronization either of a pair of mutually inhibiting Leaky Integrate & Fire models
or a pair of coupled biophysical models [9, 13]. In this report we investigate whether this behaviour is general or model
dependent. The effect of the presence of the electrical coupling on the synchronization properties of the coupled cells is
also investigated. To this aim the synchronization properties of a pair of mutually inhibiting cells are studied using four
different single cell models in the weak coupling limit. It is found that the increase of the frequency discharge does not
promotes synchronization for all the four model studied. Instead the presence of the electrical coupling always fosters the
emergence of synchronous firing.
Keywords: synchronization, interneurons, gap-junctions.
REFERENCES
[1] Gray C.M., Koning P., Engel A.K., Singer W., Oscillatory responses in cat visual cortex exhibit inter-columnar
synchronisation which reflects global stimulus properties. Nature, 338: 334-337, 1989.
[2] Cobb SR, Buhl EH, Halasy K, Paulsen O, and Somogyi P., Synchronization of neuronal activity in hippocampus by individual
GABAergic interneurons. Nature 378: 75–78, 1995.
[3] Pouille F., Scanziani M., Enforcement of temporal fidelity in pyramidal cells by somatic feed-forward inhibition.
Science 293: 1159–1163, 2001.
[4] Galarreta M., Hestrin S., Electrical synapses between GABA-releasing neurons. Nature Neurosci. 2: 425–433, 2001.
[5] Connors B.W., Long M.A., Electrical synapses in the mammalian brain. Annu. Rev. Neurosci., 27: 393–418, 2004.
[6] Jonas P., Bischofberger J., Fricker D., Miles R., Interneuron Diversity series: Fast in, fast out – temporal and
spatial signal processing in hippocampal interneurons. TRENDS in Neurosciences 27: 30-40, 2004.
[7] Wang, X. J., Buzsaki, G., Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. J.
Neurosci. 16: 6402–6413, 1996.
[8] Bartos M., Vida I., Frotscher M., Meyer A., Monyer H., Geiger J.R., Jonas P., Fast synaptic inhibition promotes
synchronized gamma oscillations in hippocampal interneuron networks. PNAS 99: 13222–13227, 2002.
[9] Lewis T.J., Rinzel J., Dynamics of spiking neurons connected by both inhibitory and electrical coupling. J Comput
Neurosci. 14: 283–309, 2003.
[10] Bem T., Rinzel J., Short Duty cycle destabilizes a half-center oscillator, but gap junctions can restabilize the
anti-phase pattern. J Neurophysiol. 91: 693–703, 2004.
[11] Kopell N.,Ermentrout B., Chemical and electrical synapses perform complementary roles in the synchronization of
interneuronal networks. PNAS 101: 15482–15487, 2004.
[12] Pfeuty B., Mato G., Golomb D., Hansel D., The Combined Effects of Inhibitory and Electrical Synapses in Synchrony.
Neural Computation 17: 633–670, 2005
[13] Di Garbo A., Panarese A., Chillemi S., Gap junctions promote synchronous activities in a network of inhibitory
interneurons. BioSystems 79: 91–99, 2005.
66.Gravitational Impact On The Retinal Spreading Depression
Wolfgang Hanke, University of Hohenheim - 230, hanke@uni-hohenheim.de
Neuronal tissue and especially the CNS (the human brain) fulfill all the requirements for excitable media. Consequently
self-organisation, pattern formation and propagating excitation waves as typical events of excitable media have been
observed in such tissue. The behaviour of these phenomena is critically depending on the parameters of the system, to
which gravity as a permanently present stimulus under terrestrial conditions belongs.
The spreading depression (SD) as a propagating excitation-depression wave of neuronal activity, which is fully reversible,
is the most obvious and best described of the above mentioned phenomena. Especially in the retina as a true part of the CNS
it can be easily observed with optical techniques due to the big intrinsic optical signal in this tissue. This allows a two
dimensional observation of the complete process in time. The influence of gravitation (micro-g, 1g, macro-g) on the
parameters of the spreading depression has been investigated in the retinal system, using the drop-tower, parabolic flights
and centrifuges due to the time course of the process. Platforms and set-ups for such experiments have been developed and
used.
The SD shows a behaviour quite similar as the well known Belousov-Zhabotinsky (BZ)-chemical reaction, which can be used as
a simplified model system for control experiments under identical conditions using the same equipment. The theoretical
(physical) background for BZ and SD is given, thus an understanding and formal description of the influence of gravity on
these systems, and thus principally on the self-organising properties of the human brain, too, seems to be reasonable.
The SD is also known to be involved in some patho-physiological events as there are among others migraine, transient
global amnesia, and some forms of epilepsy. Possible gravitational influence on these phenomena would be of great medical
interest for future space flight.
Finally, the properties of an excitable medium would allow the CNS to react directly to stimuli like gravitation,
delivering as sensor mechanism without the need of a specified gravity receptor. The SD can be used as a first approach here
to investigate the reaction of complex neuronal structures to gravity.
67.Noise-Induced Basin Hopping In Vibro-Impact Systems
Ibere Caldas, Institute of Physics, University of Sao Paulo, ibere@if.usp.br
Silvio L. T. Souza, Instituto de Fisica, USP
Ricardo L. Viana, Departamento de Fisica, UFPR
Jose M. Bhaltazar, Departamento de Estatistica, UNESP
We numerically investigate some dynamical effects of adding a certain amount of parametric noise in vibro-impact systems.
These systems have moving parts colliding with either moving or stationary components, and are often found in engineering
applications [1]. One of the most conspicuous influences on vibro-impact and, in general, on any oscillator system, is
caused by extrinsic noise, which is unavoidable in laboratory and industrial contexts. The effects of noise for simple
periodic motions are fairly well understood, and their control or suppression can be achieved by standard procedures, like
noise filtering. However, such treatments may fail for complex motions comprising periodic, quasi-periodic and chaotic
regimes, often coexisting with a complicated basin of attraction structure. One of the outstanding features in noisy
multistable systems is basin hopping, which consists of the intermittent switching between two or more basins of attraction,
when the system is subjected to noise [2]. In vibro-impact systems, in particular, basin hopping can be highly undesirable
and even dangerous, since it may produce large amplitude jumps in the oscillations of the moving parts and a consequent
fatigue of the material, if not the complete system breakdown. In our numerical simulations, we consider a theoretical
model rattling in a single-stage gearbox [3] and an impact-pair system [4]. For these systems, we have identified
coexisting of attractors with fractal boundary basins for wide range of system parameters. The addition of parametric noise
causes basin hopping, i.e. the alternate switching among different coexisting attractors. These alterations occur between
different time intervals obeying an exponential distribution. The average duration of such intervals decreases with
increasing noise level, and satisfies a scaling law [5].
[1] Blazejczyk-Okolewska B, Czolcynsky K, Kapitaniak T, Wojewoda J. Chaotic mechanics in systems with friction and
impacts. Singapore: World Scientific; 1999.
[2] Kraut S, Feudel U. Multistability, noise, and attractor hopping: the crucial role of chaotic saddles. Phys. Rev. E
2002;66:015207(R).
[3] Karagiannis K, Pfeiffer F.
Theoretical and experimental investigations of gear-rattling. Nonlinear Dynamics 1991;2:367-387.
[4] Han RPS, Luo ACJ, Deng W. Chaotic motion of a horizontal impact pair.Journal of Sound and Vibration 1995;181:231-250.
[5] de Souza SLT, Batista AM, Caldas IL, Viana RL, Kapitaniak T. Noise-induced basin hopping in a vibro-impact system.
Chaos, Solitons and Fractals, in press.
68.Smart Dampers To Supress Chaos In Dissipative Mechanical System
Silvio L.T. de Souza, Instituto de Fisica , Universidade de Sao Paulo, thomaz@if.usp.br
Ibere L. Caldas, Instituto de Fisica, Universidade de Sao Paulo
Ricardo L. Viana, Universidade Federal do Parana
We show how to suppress chaotic behavior in dissipative mechanical systems by varying the damping coefficient according to
the velocity direction. As an example application of the method, we present numerical simulations of an impact oscillator
and the required damping law used to achieve the control. Our numerical results show the method effectiveness even for high
levels of noisy perturbation.
69.Control Of A Chaotic Chua's Circuit To Perform Logic Operations
Abraham Miliotis, University of Florida - Biomedical Engineering, am397@ufl.edu
We present experimental results of a chaotic circuit realization of the fundamental NOR gate. A simple threshold mechanism
applied on the chaotic Chua's circuit, at a value dependant on the inputs, yields a behavior of the circuit analogous the
input-output relations of the NOR gate. We also present simulation results which show that connecting Chua's circuits
together, according to the same mechanism, the desired input-output relationships are accomplished. Specifically we present
results for the combination NOR(NOR(I1,I1),NOR(I2,I2)) = AND(I1,I2).
References:
[1]* K. Murali, S. Sinha, and W. L. Ditto, Implementation of NOR gateby a chaotic Chua's circuit, Int. J. of Bifurcation
and Chaos, 13(9), 2669-2672, 2003.
[2]* K. Murali, S. Sinha, and W. L. Ditto, Realization of the fundamental NOR gate using a chaotic circuit, Phys. Rev.
E 68, 016205, 2003.
[3]* K. Murali, S. Sinha, and W. L. Ditto, Construction of a recon¯gurable dynamic logic cell, Pramana, 64(3), 433-441, 2005.
70.Active Control With Delay Of Catastrophic Motion And Horseshoes Chaos On An Euler Beam Using Piezoelectric Absorber
B. R. Nana Nbendjo, Present institution: Departemanto de fisica, Universidade Federale do Parana, C.P 81531-990 Curitiba,
Brazil, brnana@fisica.ufpr.br
P. Woafo, Laboratory of Nonlinear Modeling and Simulation in Engineering and Biological Physics, Faculty of Sciences,
University of Yaoundé I, PO Box 812 Yaoundé, Cameroon
In this Communications, the control of escape and Melnikov chaos of a hinged-hinged beam is considered. Piezoelectric
ceramics have been chosen as Activators. The effect of time-delay between the detection of vibration and action of the
control is particularly investigated. The approximate critical external forcing amplitudes for catastrophe and chaos are
obtained by using the energy and Melnikov methods. The control efficiency is found by analyzing the behaviors of the
external critical forcing amplitude of the controlled system as compared to that of the uncontrolled system.
71.Experimental Investigation Of A Nonlinear Pendulum
Marcelo Savi, COPPE/UFRJ, savi@mecanica.ufrj.br
Aline Souza de Paula, COPPE/UFRJ
Francisco Heitor I. Pereira-Pinto, IME
Chaos may occur in many natural processes and the idea that chaotic behavior may be controlled by small perturbations of
some physical parameter is making this kind of behavior to be desirable in different applications. This contribution
analyzes the dynamical response of a nonlinear pendulum. Single and double pendulums are considered. Basically, the
pendulum consists of an aluminum disc connected to a rotary motion sensor and a magnetic device provides adjustable energy
dissipation. A string-spring device provides torsional stiffness and also, together with an electric motor, excites the
system. The double-pendulum is constructed connecting a bar to the disc. This system provides a picture where chaos may be
considered as an interesting response of mechanical system. Mathematical modeling is carried out and numerical simulations
are in close agreement with experimental data. Moreover, state space reconstruction is performed for single and double
pendulum showing the differences in the analysis.
72.Regular And Chaotic Regions In The Space Phase Of An Anharmonic Sextic Driven Oscillator
Juliano Antônio de Oliveira, Universidade Estadual Paulista - UNESP - Brazil, juliano@feg.unesp.br
Othon Cabo Winter, Universidade Estadual Paulista - UNESP - Brazil
Alvaro de Souza Dutra, Universidade Estadual Paulista - UNESP – Brazil
The study of dynamical systems became interesting to several authors in the last years, especially the analysis in the
classic limit of dynamical systems that have classic chaotic behavior. In this work we propose to start the study of the
regular and chaotic regions in the phase space of an anharmonic sextic driven oscillator. We define a Hamiltonian to the
classic dynamic of a particle under the action of an external force in this double-well potential. An initial motivation to
study the sixth-order potential is that in quantum mechanics it is the simplest polynomial potential that belongs to the
class of the quasi-exactly-solvable potential. The characteristic of such potential is to have exact solutions of the
Schroedinger equation for the first "n" (n integer arbitrary finite) levels of energy of the potential, provided that their
parameters obey certain restrictions. From the Hamiltonian we write the equations of motion to built the Poincaré sections,
in which we identify the presence of internal and external islands in the chaotic region. We get the time evolution of the
displacement, of the energy and we check the results in the symmetrical double-well potential, classifying the islands as
being resonant and nonresonant. The nonresonant islands are located at the bottom of double-well potential determining that
there, the motion corresponds to that of a harmonic oscillator. We vary the anharmonic parameter and verify that for their
lower values, the chaotic region increases, while the variation of the elastic constant coefficient of the system produces
a size increasing of the nonresonant islands. We intend to go further on this work and the next step is to study the
classic-quantum correspondence through the computation of the time evolution of the Husimi function, to check the coherent
tunneling between islands of same nature presents in the Poincaré sections.
KEYWORDS: Anharmonic sextuple driven oscillator; Poincaré sections; Chaos.
73.A Chaotic Behavior Of A Non-Ideal Spinup Through Resonance
José Manoel Balthazar, UNESP Rio Claro, jmbaltha@rc.unesp.br
Silvio Thomas de Souza, IF-USP-SP
Ibere Luiz Caldas, IF-USP-SP
RL Viana, IF-Ufe Paraná Curitiba
R. Brasil, Escola Politécnica USP-SP
A Experimental analysis of a non-ideal cantilever beam, that is, excited by a DC motor of limited power supply (Non_ideal)
which those elements are Cantilever Beam Parameters: Material: SAE 1030 Steel, Length: 430 mm, Width: 50.8 mm, Thickness:
6.35 mm and Natural Frequency: 7.5 Hz. And Motor Characteristics: Weight of the 2 disks: 1586 g, Weight of the unbalanced
masses: 50 g, Weight of the motor: 1674 g, Moment of Inertia of the rotor axis: 1.3E-005 kg mm.Total Weight: 3310 g and
Distance of the unbalanced masses from center of the motor: 80 mm. Have been proved based on those cubic and quadratic
nonlinearities are present in the dynamical system are of same n order of magnitude. This fact is important to modeling
safety the problem.
Based on these results an idealized model of a one-dimensional motion of a cart of mass M connected to frame by a nonlinear
spring and a dash-pot (viscous) is considered. The motion of the cart is due to an in-board non-ideal motor with moment of
inertia J and driving an unbalanced rotor.
We present a procedure to suppress chaotic behavior in non-ideal oscillators. For that, we use a small-amplitude signal
associated with power supply in such way the control signal alters the characteristic curve of the motor. This method is
based in the fact that, altering the oscillator's averaged energy, one can steer the system trajectories from a chaotic
attractor to a periodic orbit which would give improved system performance. In the application presented, the proposed
method works efficiently for a large range of control parameters.
74.How One Can Use Di Quark Scalar Fields Permitting A Cosmological Constant In Line With Actual Known Observational Values
Andrew Beckwith, APS+ Fermi research contractor( Partial affiliation with lab), projectbeckwith2@yahoo.com
General Relativity and Quantum Cosmology,arXIV abstract, gr-qc/0603021
Comments: 11 pages, 2 figures, and is a write up of an idea created due to lecture I attended by Dr. Steinhardt as a
participant in the UCLA dark matter conference, 2006 with respect to implications of an update of Abbots 1985 work with the
cosmological constant.
We previously showed that we can use di quark pairs as a model of how nucleation of a new universe occurs. We now can
construct a model showing how a di quark condensate can be used to formulate a cosmological constant more in line with
known physical observations instead of the manifestly huge value obtained vial Quantum Chromodynamics These results are
consistent with applying Abbots criteria of a bound for the cosmological constant without his enormous tunneling time value
which effectively caused his model to be abandoned as unworkable in the mid 1980s. This is in part due to a phase
transition alluded to by Dr. Edward Kolbs model of how the initial degrees of freedom declined from over 100 to something
approaching what we see today in flat space cosmology. That phase transition would be a bridge from a tilted washboard
potential to the chaotic inflationary model pioneered by Guth which is congruent with the
75.How Soliton-Anti Soliton Di Quark Pairs Signify An Einstein Constant Dominated Cosmology, And Lead To New Inflationary
Cosmology Physics
Andrew Beckwith, APS, projectbeckwith2@yahoo.com
General Relativity and Quantum Cosmology, abstract gr-qc/0511081
Comments: 45 pages, 3 figures, very expanded version of material in accepted PANIC 2005 talk at Santa Fe, NM, which will in
abbreviated form be in AIP published proceedings for PANIC 2005
We review the results of a model of how nucleation of a new universe occurs, assuming a di quark identification for
soliton-anti soliton constituent parts of a scalar field. Initially, we employ a false vacuum potential system; however ,
when cosmological expansion is dominated by the Einstein cosmological constant at the end of chaotic inflation, the initial
di quark scalar field is not consistent with respect to a semi classical consistency conditions we analyze as the potential
changes to the chaotic inflationary potential utilized by Guth. We use Scherrer's derivation of a sound speed being zero
during initial inflationary cosmology, and obtain a sound speed approaching unity as the slope of the scalar field moves
away from a thin wall approximation. All this is to aid in a data reconstruction problem of how to account for the initial
origins of CMB due to dark matter since effective field theories as presently constructed require a cut off value for
applicability of their potential structure. This is often at the cost of, especially in early universe theoretical models,
of clearly defined baryogenesis, and of a well defined mechanism of phase transitions.
76.Alternative Paths For Insertion Of Probes In High Inclination Lunar Orbits
Cristiano Fiorilo de Melo, LAC/INPE - FAPESP Pos doc Program , cristianofiorilo@terra.com.br
Elbert E. N. Macau, LAC/INPE
Othon Cabo Winter, FEG/UNESP
The dynamics of the circular, planar, restricted three-body Earth-Moon-particle problem predicts the existence of direct
periodic orbits around the Lagrangian equilibrium point L1. From these orbits, derive a group of paths that form links
between the Earth and the Moon. Moreover, they are capable of carrying out transfers between terrestrial and lunar orbits
of low altitudes. When we considered more complex dynamical systems, such as the three-dimensional full four-body
Sun-Earth-Moon-probe problem, which takes into account, besides other factors, the inclination of the orbit of the Moon,
these paths, leaving terrestrial orbits of low altitudes (LEO), gain inclination when they penetrate in the sphere of lunar
influence allowing the insertion of probes in lunar orbits of high inclinations and low altitudes. In spite of the chaotic
behavior of these paths, we studied your properties giving emphasis to two types of transfer maneuvers. Firstly, we
investigated direct transfers by inserting probes in lunar orbits with inclinations varying between 29o and 42o. Next, we
investigated directed transfers with the application of a DV along of the trajectory in order to lead the probe into lunar
orbits with inclinations between 0o and 180o. The results allowed the definition of a group of paths capable of carrying
out Earth-moon transfers with flight time between 13 and 16 days with relatively low costs.
77.Polar Cusp Response To Solar Wind Variability
Ezequiel Echer, Instituto Nacional de Pesquisas Espaciais, eecher@dge.inpe.br
Axel Korth, Max Planck Institut fuer Sonnensystemforschung
Walter D. Gonzalez, Instituto Nacional de Pesquisas Espaciais
Fernando L. Guarnieri, Instituto Nacional de Pesquisas Espaciais
In this work we present a study of the Earth's polar cusp response to solar wind variability during the month of February
2001. Magnetic field and plasma observations in the magnetospheric cusps are from detectors onboard the Polar and Cluster
spacecraft. Solar wind data are taken from instruments onboard ACE spacecraft. We use wavelet techniques to study the
non-steady polar cusp response to the passage of different solar wind structures. Hydrogen ion (H+) energy and pitch angle
spectrograms from CIS/Cluster are analysed during disturbed and quiet periods. In special, the occurrence of non-linear
Alfven waves during corotating interaction region high speed streams in the solar wind and in the polar cusp is
investigated.
78.Stable Regions In Pluto-Charon System
A. H. F. GUIMARÃES , UNESP - Grupo de Dinâmica Orbital e Planetologia, anah@feg.unesp.br
S. M. GIULIATTI-WINTER , UNESP - Grupo de Dinâmica Orbital e Planetologia and INPE - São José dos Campos/ Brazil
Pluto, Charon and the new discovered satellites S/2005 P1 and S/2005 P2, are targets of micrometeoroids, which are probably
originate from the Kuiper Belt zone. The impacts onto their surfaces should immediately release a cloud of ejected dusts
around the system. The goal of the present work is to determine stable regions where these dust particles can stay for a
long period of time. The analysis will be performed by using the technique of Poincaré’s Surface of Section, which indicate
the stable and chaotic regions. The internal and external regions of the binary system are considered, including the region
where the new satellites P1 and P2 are located. From Poincaré’s Surface of Section the diagrams of Cj X x were obtained,
with unable us to determine, for a set of Cj values (Jacobi’s constant), the stable regions. The results show that the
region with a < 8000km is stable. For those particles orbiting the satellite Charon the stable region extends until
a=2500km. Outside the binary system, the stable region starts at a > 42000km. From these results we verified that the
discovered satellites are located in a stable region.
79.Observation And Theory Of Chaos In Solar And Planetary Radio Emissions
Rodrigo A. Miranda, National Institute for Space Research (INPE) and World Institute for Space Environment Research
(WISER), rmiranda@dge.inpe.br
Abraham C. L. Chian, National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER)
Erico L. Rempel, Institute of Aeronautical Technology (ITA), Sao Jose dos Campos - SP, 12228-900 Brazil
Observational data from solar radio emissions have presented chaotic signatures. Kurths and Karlicky (1989), using data
from the Tremsdorf Solar Radio Observatory during a type IV solar radio burst, obtained positive values for the maximum
Lyapunov exponent which indicates the presence of deterministic chaos. Isliker and Benz (1994), using data from several
solar events involving radio emissions from the spectometer IKARUS at Zurich, found that during solar radio bursts the
temporal time series exhibit intermittent patterns. Kurths and Schwarz (1994) showed that solar radio bursts detected at
the Metsahovi Radio Research Station (Helsinki) exhibit non-stationary or transient behavior, which is characteristic of
chaotic systems.
Nonlinear wave-wave interactions can be a source of radio emissions. Theoretical studies of generation of solar and
planetary radio emissions have been carried out. Chian et al. (2000) studied a model for the nonlinear 3-wave interactions
involving Langmuir, whistler and Alfvén waves, and its evolution from orderly to chaotic behaviors. In Chian et al. (2002),
two types of intermittency were recognized in the numerical simulation of plasma emissions. Miranda et al. (2005)
investigated the phenomenon of intermittency for a nonlinear model of 4-wave interactions.
In this work we study the temporal dynamics of nonlinear 3-wave interactions involving one linearly unstable mode and two
linearly damped modes having different damping rates in space plasmas. First, we construct a bifurcation diagram by choosing
the damping rate of the second induced wave as our control parameter, and keeping all other system parameters constant.
Then, we show the occurrence of two types of intermittency: the type-I Pomeau-Manneville, and the crisis-induced
intermittency. Finally, the average time between intermittent events is calculated for different values of the control
parameter, for each type of intermittency. The results presented in this study can improve our understanding of the
intermittency frequently observed in chaotic time series from solar and planetary radio emissions.
References:
[1]Chian, A. C.-L.; Borotto, F. A.; Lopes, S. R.; Abalde, J. R. Chaotic dynamics of nonthermal planetary radio emissions.
Planetary and Space Science 48, 9-21, 2000
[2]Chian, A. C.-L.; Rempel, E. L.; Borotto, F. A. Chaos in magnetospheric radio emissions. Nonlinear Processes in
Geophysics 9, 435-441, 2002
[3]Isliker, H; Benz, A. O. On deterministic chaos, stationarity, periodicity and intermittency in coronal bursts and
flares. Space Science Reviews 68 (1-4), 185-192, 1994
[4]Kurths, J; Karlicky, M. The route to chaos during a pulsation event. Solar Physics 119 (2), 399-411, 1989
[5]Kurths, J; Schwarz, U. Chaos theory and radio-emission. Space Science Reviews 68 (1-4), 171-184, 1994
[6]Miranda, R. A.; Rempel, E. L.; Chian, A. C.-L.; Borotto, F. A. Intermittent chaos in nonlinear wave-wave interactions in
space plasmas. Journal of Atmospheric and Solar-Terrestrial Physics 67, 1852-1858, 2005
80.The Orbital Fit Of Wandering Moonlets
Othon Winter, UNESP, ocwinter@feg.unesp.br
Décio C. Mourão, UNESP
Silvia M. Giuliatti Winter, UNESP
Frank Spahn, Universität Potsdam
Cristiano F. da Cruz, UNESP
Recent images from Cassini spacecraft show bright clump-like features at different locations within Saturn's narrow F ring.
The images do not have enough resolution to distinguish whether these features are solid moonlets or just rubble piles of
boulders and dusty loose clump of particles. “Some of these features seem to cross the whole ring”. The complex evolution of
the observed features, obtained from sequences of images, did not allow the determination of their orbits. Planetary
dynamicists have long proposed that some of the unusual structures observed in the F ring are produced by moonlets hiding
inside the ring. However, the trajectories of such moonlets were not explored. Here we show that the features detected
through Cassini camera images might be moonlets that present chaotic orbital evolution due to the gravitational interaction
with the nearby satellites Prometheus and Pandora. The moonlets present a very short Lyapunov time (the e-folding time for
divergence of nearby orbits) of the order of only a few 100 orbital periods. We show that, despite of having a highly
chaotic behaviour, more than 93% of the moonlets remain confined nearby the F ring owing to a very low radial diffusion
contrasted by a rather high longitudinal dispersion.
81. Bursting behavior in a laser: control and synchronization.
Riccardo Meucci , CNR- Istituto Nazionale di Ottica Applicata , ric@ino.it
F. Salvadori , Dept. of Physics, University of Florence
K. Al-Naimee , Dept. of Physics, College of Sciences, University of Baghdad
F. T. Arecchi, Dept. of Physics, University of Florence
Bursting behavior, characterized by intermittent transitions between two regimes with different amplitudes, is a common
feature in many fields of science. Here we present two different topics related to bursting,namely, its control and
synchronization.
Recently controlling multistability and crisis induced intermittency (bursting behavior) have been experimentally proved in
a modulated class B laser by means of a feedback method [1]. This method relies on the knowledge of the frequency components
of the two attractors in a bistable regime or orbits competing in the same chaotic attractor near an interior crisis. The
presented method can be applied in different systems as in the epidemiological models like the SEIR considering its
topological equivalence with the modulated laser [2].
Experimental synchronization between two lasers in a bursting regime has been demonstrated in different schemes, including
master-slave and bidirectional coupling [3]. The coupling between the two lasers occurs by means of amplitude modulation of
the driving signal. The analysis has been performed by studying the inter-bursting times.
[1] R. Meucci, E. Allaria, F. Salvadori, and F. T. Arecchi, Phys. Rev. Lett. 95, 184101 (2005).
[2] L. Billings, E. Bollt, D. Morgan, and Ira B. Schwartz, in Proceedings of the Fourth International Conference on
Dynamical Systems and Differential Equations,(Wilmington, NC, USA, 2002), p. 122.
[3] R. Meucci, F. Salvadori, F. T. Arecchi, K. Al-Naimee, and S. Boccaletti, submitted.
82. Modeling of the dynamics of Euler beams by F6 potential: catastrophic motion and Smale horseshoes chaos in a model
B. R. Nana Nbendjo, Present institution: Departemanto de fisica, Universidade Federale do Parana,
C.P 81531-990 Curitiba, Brazil. , brnana@fisica.ufpr.br or brnana@uycdc.uninet.cm
P. Woafo, Laboratory of Nonlinear Modeling and Simulation in Engineering and Biological Physics,
Faculty of Sciences, University of Yaoundé I, PO Box 812 Yaoundé, Cameroon.
We derive in this communication the mathematical model, describing the single mode dynamics of a beam subjected to external
loads. Taking into account the geometrical nonlinearities and considering the second order approximation of the deflected
length of the beam, we show that the single mode dynamics of a simply supported (hinged-hinged) beam can be described by a
F6 potential with various configurations. The conditions in the space parameters of the system for which catastrophic
motion (escape from a potential) occur along with Smale horseshoes chaos are derived an verified by direct numerical
simulation of the base equation.
83. Characteristics of Bursts in Tokamak Electrostatic Turbulence
Zwinglio O. Guimarães-Filho, IFUSP, zwinglio@if.usp.br
Gustavo Z. S. Lima, IFUSP
Iberê L. Caldas, IFUSP
Maria Vittoria A.P. Heller, IFUSP
In tokamaks, there are evidences that part of the particle transport may be convective, associated to plasma structures
whose propagation are responsible for the intermittent bursts commonly observed in the electrostatic fluctuation signals
registered by the Langmuir probes. Thus, it is important to determine the spatial and temporal scales of these bursts and
their dependence on the plasma radial position. To do that, in this work we consider data measured by Langmuir probes in the
tokamak TCABR* [I.C.Nascimento et al., Nucl. Fusion 45 (2005) 796]. From these data, we analyse the fluctuating plasma
density, burst radial velocities, and induced particle transport. The probability distribution functions (pdf) of these
fluctuations are clearly skewed, reflecting the occurrence of numbers of high amplitude positive fluctuations much greater
than what is expected from a Gaussian distribution obtained for random distributions. The observed skewness is more
pronounced in the scrape-off layer than in the plasma edge. Moreover, these pdf have a Gaussian negative side indicating
that there are no negative fluctuations associated to the bursts. Furthermore, in our analysis, the intermittent bursts are
selected by an amplitude criterion (2.5 times its standard deviation). The conditional averaging is used as a statistical
tool to determine the main features of the selected bursts, as their rising and decay times. In the scrape-off layer
(outside the plasma limiter) the bursts of the fluctuating plasma density present rising times higher then their decay
times, as observed in other tokamak discharges. However, at the plasma edge these bursts are almost symmetric in time,
i.e., the increase and decrease times are practically the same. Moreover, for the other fluctuation (induced particle
transport, and plasma radial velocity), both at the plasma edge and in the scrape-off layer, the burst shapes are also
symmetric.
* We acknowledge the TCABR-Team for the collaboration choosing the data used in this work
84. Synchronization in a Network of Chua´a Circuits
Cornelio Posadas-Castillo, Engineering Faculty, Baja California Autonomous University (UABC), México,
FIME University Autonomous of Nuevo León (UANL), México, cposadas@uabc.mx
César Cruz-Hernández , Telematics Direction, Scientific Research and Advanced Studies Center of Ensenada (CICESE), México.
Rosa Martha López Gutiérrez, Engineering Faculty, Baja California Autonomous University (UABC), México
Chaos synchronization has attracted much attention in recent years see e.g., [1] and references therein. This property is
supposed to have interesting applications in different fields, particularly to design secure communication systems.
On the other hand, synchronization in networks of coupled chaotic dynamical systems has received a great deal of attention
in recent years, particularly are of significant interest in many fields of science and technology [2]-[5].
In this work, the synchronization problem in a network of coupled Chua´s circuits in master-slave configuration, from the
perspective of Generalized Hamiltonian forms and observer approach is numerically and experimentally studied. The approach
allows to give a simple design procedure for the slave system and clarifies the issue of deciding on the nature of the
output signal to be transmitted. This may be accomplished on the basis of a simple linear detectability or observability
test. We enumerate several advantages over the existing synchronization methods: i) It enables synchronization be achieved
in a systematic way, ii) it can be successfully applied to several well-known chaotic systems, iii) it does not require the
computation of any Lyapunov exponent, and iv) it does not require initial conditions belonging to the same basin of
attraction.
The Generalized Hamiltonian nature of many chaotic systems definitely helps in the study of robust synchronization, under
the addition of masked transmitted signals seen as perturbations of the state reconstruction error dynamics.
In particular, Chua´s circuit [6] is chosen as the cells implemented from this new perspective and their possibilities for
synchronization of a large number of cells are confirmed. Also, we present a synchronization stability analysis.
REFERENCES
[1] Pecora L.M. & Carroll T.L. “Synchronization in chaotic systems,” Phys. Rev. Lett. 64, 1990, 821-824; Special Issue on
Chaos synchronization and control: Theory and applications, IEEE Trans. Circuits Syst. I, 44(10), 1997; Special Issue on
Control and synchronization of chaos, Int. J. Bifurc. Chaos, 10(3-4), 2000; C. Cruz-Hernández & H. Nijmeijer,
Synchronization through filtering, Int. J. Bifurc. Chaos, 10(4), 2000, 763-775; Sira-Ramírez H. & Cruz-Hernández C.,
Synchronization of chaotic systems: A Generalized Hamiltonian systems approach, Int. J. Bifurc. Chaos, 11(5),
2001, 1381-1395; López-Mancilla D. & Cruz-Hernández C. Output synchronization of chaotic systems: Model-matching approach
with application to secure communication, Nonlinear Dynamics and Systems Theory, 5(2), 2005, 141-156; Feldmann U., Hasler M.
& W. Schwarz “Communication by chaotic signals: the inverse system approach,” Int. J. Circuits Theory and Applications, 24,
1996, 551-579; Nijmeijer H. & Mareels I.M.Y. “An observer looks at synchronization,” IEEE Trans. Circuits Syst.I, 44(10),
1997, 882-890.
[2] Wu C. W. Synchronization in coupled chaotic circuits and systems, World Scientific 2002.
[3] Wang X. F. “Complex networks: topology, dynamics, and synchronization,” Int. J. Bifurc. Chaos, 12(5), 2002, 885-916.
[4] Wang X. F. & Chen G. “Synchronization in small-world dynamical networks,” Int. J. Bifurc. Chaos, 12(1), 2002, 187-192.
[5] Posadas-Castillo, C. Cruz-Hernández & López D. "Synchronization of chaotic neural networks: A Generalized Hamiltonian
systems approach", Procs. of the International Conferenceon Fuzzy Systems, Neural Networks and Genetic Algorithms (FNG2005),
Springer-Verlag 2005.
[6] Cruz-Hernández C., López, García V.,Serrano H. & Núñez R. “Experimental realization of binary signal transmisión using
chaos,” J. Circuits, Syst. Computers 14(3) 2005 453-468.
85. Regularization of an Automatic Pilot Model
Marcos Cesar Vergès, Universidade Federal do Paraná, mcverges@bol.com.br
Ricardo Luiz Viana, Universidade Federal do Paraná
In this work we applied a regularization algorithm in a classic discontinuous model of automatic pilot that produce a
continuous model and where we can use the classic theory of dynamical systems to make the analysis.
86. Stability of Periodic Orbits in a periodically Forced Mechanical System with Unstable Dimension Variability
Geraldo Kubo, Universidade Federal do Paraná, geraldokubo@yahoo.com.br
Geraldo Takachi Kubo, Universidade Federal do Paraná
Cristiano Francisco Woellner, Universidade Federal do Paraná
Sergio Roberto Lopes, Universidade Federal do Paraná
Ricardo Luiz Viana, Universidade Federal do Paraná
We considered a mechanical system consisting of a periodically kicked double rotor, described by a four-dimensional
non-invertible map. We analysed the stability of period-1 and period-2 orbits for the system, and compared our
results with bifurcation diagrams both for the phase-space as well as the Lyapunov exponents. Our major goal is to describe
the onset of Unstable Dimension Variability, and the situation where this effect is most intense.
87. Van der Pol’s Equation in Self-Excited Electron-Wave Oscillators
Joaquim J. Barroso, National Institute for Space Research (INPE), barroso@plasma.inpe.br
Generation of high-power microwave has remained an active area of research common to both scientific and industrial
applications, including high-resolution radars, particle accelerators, deep space communication systems, materials
processing, and controlled thermonuclear fusion. Much emphasis has been placed on microwave generators that do not
require an external magnetic field so as to reduce cost, size and weight of the device. One such device is the monotron,
which is a self-excited oscillator consisting of an electron beam that transits across a resonant cavity, which plays the
part of a tank circuit of an ordinary RLC oscillating circuit. The monotron lumped equivalent circuit can be thought of as
consisting of a physical tuned circuit connected to a resistor of negative resistance. For transit times near (N+1/4)T,
where N is an integer and T the oscillation period, electron bunches are formed and upon reaching the cavity’s end plate in
a decelerating phase of the RF field the bunches transfer energy to the cavity. The relation between voltage and current is
set by the beam admittance, which is always non linear, so that for one amplitude will there be a given ratio between
current and voltage. From the equation of motion of the beam electrons interacting with the RF fields, such relation [the
electronic beam nonlinear admittance Y(V^2)] is found by expanding the conversion efficiency up to the tenth power of the
RF voltage amplitude. Then using Y(V^2) in the energy balance equation (relating the RF power losses in the cavity and the
microwave power radiated by the electron beam) we arrive at the van der Pol’s equation, just describing the non linear
growth and the stationary generation of the electromagnetic mode operating in the cavity driven by the externally injected
beam. It is shown that the analytic expressions for the self-excitation condition and for the saturation of the wave growth
found on the basis of a 1-D circuit model are in excellent agreement with a full scale 2.5-D particle-in-cell simulation.
88. Using chaos to reduce oscillations
Tomasz Kapitaniak, Division of Dynanamics, Technical University of Lodz, tomaszka@p.lodz.pl
We present the new design of the impact damper. The damper is designed in such a way that it allows the replacement of the
periodic impactless oscillations with a large amplitude, by the chaotic impact motion with very small amplitude. We give
experimental evidence of the effectiveness of our method.
89. Origin of chaotic dynamics of two interacting particles in a one-dimensional billiard
César Manchein, Universidade Federal do Paraná, cmanchein@fisica.ufpr.br
Marcus W. Beims, Universidade Federal do Paraná
Jan M. Rost, Max Planck Institute for the Physics of Complex Systems
We study the classical dynamics of two unequal-mass particles in a one-dimensional billiard. It is known that ergodicity
may be obtained in point-like collisions for specific mass ratios ?=m_2/m_1, and that Lyapunov exponents are zero. However,
if a Yukawa interaction between the particles is introduced, positive Lyapunov exponents are found and change with the
masses ratio between particles. While the largest finite-time Lyapunov exponent changes smoothly with ?, the most probable
one, extracted from the distribution of finite-time Lyapunov exponents over initial conditions, reveals details about the
phase space dynamics.
90. Wildland fire behaviour modeling using lumped parameter approach
Rodolfo Maduro Almeida, Curso de Pos-graduação em Computação Aplicada - INPE,rodolfo@lac.inpe.br
Issamu Muraoka, Divisão de Mecânica Espacial e Controle - INPE
Fernando M. Ramos, Laboratório Associado de Computação e Matemática Aplicada - INPE
Elbert E. N. Macau, Laboratório Associado de Computação e Matemática Aplicada - INPE
This work displays the methodology used in the elaboration of a surface fire spread model. The mathematical method used in
the modeling is the lumped parameter approach. In this method the thermal domain is divided in a finite number of volumes,
supposed isothermal and with homogeneous properties, called nodes. To each node are attributed a temperature, a thermal
capacitance and possibly internal heat generation. The nodes interact between themselves and with the environment exchanging
heat by conduction, convection and radiation through a matrix of conductances. A system of differential equations
represents the thermal balance of heat enchanges for each node. The solution of this system represents the temporal
evolution of the temperature of the nodes. Each node exchanges heat with its neighbors through conductive condutances, with
the ambient air through convective conductances and interacts with the flames through radiativas conductances. When the
node reach the temperature of ignition, it is subject to an internal heat generation that keeps on until total consumption
of the vegetal fuel. In regard of the radiative exchanges, the flames are modeled a wall on the node, with inclination and
height dependent on the wind and the fuel consumption. The flame has the same temperature as the node. The system of
equations, representing the net heat balance of the nodes, is numerically solved, yielding, among other results, the
temporal evolution of the flame on the surface. The conductance matrix, as well as the thermal capacitances and the
internal heat generation, is updated each time step. After the implementation of the computational model, is intended to
search a form to validate it in laboratorial scale so that later it can br adapted for wildland fire behaviour modeling.
91. Spatial Recurrence Plots
Diógenes Vasconcelos, Universidade Tecnológica Federal do Paraná, vasconcelosborges@yahoo.com.br
R. L. Viana, Universidade Federal do Paraná
S. R. Lopes, Universidade Federal do Paraná
J. Kurths, Universität Postdam
We propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of
spatial patterns at a fixed time. We introduce spatial recurrence plots (SRPs) as a graphical representation of the
pointwise correlation matrix, in terms of a two-dimensional spatial return plot. This technique is apllied to the study of
complex patterns generated by coupled map lattices, which are characterized by measures of complexity based on SRPs. We
show that complexity measures we propose for SRPs provide a systematic way of investigating the distribution of spatially
coherent structures, such as syncronization domains, in lattice profile. This approach has potencial for many more more
applications, e.g., in surface roughness analyzes.
92. Transition to Chaotic Scattering and the Differential Cross-Section
Adriane Beatriz Schelin, USP, schelin@if.usp.br
Alessandro P. S. de Moura, University of Aberdeen
Celso Grebogi, University of Aberdeen
Chaotic scattering is an important manifestation of chaos present in a large variety of areas. Examples are found in fluid
dynamics, optics, molecular dynamics and atomic physics, to name a few. Although much has been done in the study of chaotic
scattering, most of the previous work concerns properties of individual orbits. In experiments, however, it is often
impossible to have access to single trajectories. In a typical situation the quantity measured is the differential
cross-section. In this work we show, by numerical simulations, that the transitions from regular to non-hyperbolic chaotic
scattering and to hyperbolic chaotic scattering is marked by a well defined signature of bifurcations in the differential
cross-section.
93. Oscillatory Kinetics in Electrocatalytic Systems
Hamilton Varela, IQSC-USP, varela@iqsc.usp.br
A. L. Martins, IQSC-USP
R. Nagao, IQSC-USP
E. F. Sitta, IQSC-USP
Many electrochemical systems are known to display complex dynamics in the form of multi-stability and oscillations in some
parameter range. The electrooxidation of small organic molecules deserves special place among the electrocatalytic reactions
because of its relevance in fuel cell research. Given the common occurrence of overlap between the adsorption isotherms of
different reaction intermediates, this class of system is particularly susceptible to undergo kinetic instabilities. We
present an overview of the recent work in our laboratory on the complexities associated to the electrooxidation reactions of
methanol and formic acid on platinum surfaces. Bi-stability between low and high reaction rates were observed in both cases
under quasi-stationary potentiostatic conditions. A very rich scenario was observed in the oscillatory regime under both
galvanostatic and potentiostatic control, including harmonic, relaxation-like and mixed mode oscillations. It has been
observed that, for methanol, oscillations occur in a narrow parameter range and depend on the subtle balance between the
anion and organic coverages. For the case of formic acid, oscillations are found in a wider parameter range and in
virtually any electrolyte composition investigated, but the oscillation morphology and the transitions among different
states are strongly correlated to the anions present in the electrolyte.
94. Chaos from a Randomly Driven RLC Filter
Jonathan Blakely, US Army RDECOM, jonathan.blakely@us.army.mil
Ned Corron, US Army RDECOM
Scott Hayes, US Army RDECOM
Shawn Pethel, US Army RDECOM
A linear, second-order filter driven by randomly polarized pulses is shown to generate a waveform that is chaotic under
time reversal. That is, the filter output exhibits determinism and a positive Lyapunov exponent when viewed backward in
time. The filter is demonstrated experimentally using a passive electronic circuit, and the resulting waveform exhibits a
Lorenz-like butterfly structure.
95. Topological analysis of signals from an erbium doped fiber ring laser
Marc LEFRANC, Laboratoire PhLAM (CNRS/Université Lille 1), marc.lefranc@univ-lille1.fr
Javier USED, Dpto Fisica Applicada, Facultad de Ciencias, Universidad de Zaragoza, SPAIN
Juan Carlos MARTIN, Dpto Fisica Applicada, Facultad de Ciencias, Universidad de Zaragoza, SPAIN
The response of an erbium-doped fiber unidirectional ring laser under sinusoidal pump modulation has been studied
experimentally for different combinations of modulation parameters (amplitude, mean value and frequency of the modulated
pump power) leading to chaotic behavior. A topological analysis has been applied to the signals observed: unstable periodic
orbits were extracted from the time series, their linking numbers in a reconstructed 3D phase space were computed and
finally the simplest template (a branched manifold describing how stretching and squeezing organize a strange attractor)
compatible with the invariants was determined.
A variety of dynamical behaviors has been found, ranging from regimes described by the standard horseshoe template or the
spiral three-branch template already observed in laser experiments to a S-shaped three-branch template not yet evidenced in
an experimental system. This template is remarkable in that it carries isotopic copies of all knots.