R.S. Cintra, H.F. de Campos Velho (2008): Breeding and predictability in chaotic dynamics. Brazilian Congress on Applied and Computational Mathematics (CNMAC-2008), September 08-11, Belem (PA), Brazil.

Abstract: One of the basic tenets of science is making predictions. If we know previous behavior, how can we predict future behavior? Predictability is an indication of the instability of the underlying flow computed from a numerical model, where small errors in the initial conditions (or imperfections in the model) grow to large amplitudes in finite times. Bred vectors are the difference between two nonlinear model integrations, periodically rescaled to avoid nonlinear saturation of the instabilities of interest. This paper presents applications of breeding vectors in a Lorenz system and a three coupling waves model for solar activities connected to the space weather process. The bred vector growth can be used to reliably predict which will be the last orbit in each of the two regimes and how long will the next regime last. The purpose of this paper is to describe the breeding method that explores chaotic model predictability.