Convergence Criterium of Numerical Chaotic Solutions Based on Statistical Measures

• Autores: Bastos de Figueiredo, Julio Cesar; Diambra, Luis Anibal; Coraci Pereira, Malta
• Año de publicación: 2011
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Chaotic Attractor; Statistical Measure; Numerical Integration
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

Solutions of most nonlinear differential equations have to be obtained numerically. The time series obtained by numerical integration will be a solution of the differential equation only if it is independent of the integration step h. A numerical solution is considered to have converged, when the difference between the time series for steps h and h/2 becomes smaller as h decreases. Unfortunately, this convergence criterium is unsuitable in the case of a chaotic solution, due to the extreme sensitivity to initial conditions that is characteristic of this kind of solution. We present here a criterium of convergence that involves the comparison of the attractors associated to the time series for integration time steps h and h/2. We show that the probability that the chaotic attractors associated to these time series are the same increases monotonically as the integration step h is decreased. The comparison of attractors is made using 1) the method of correlation integral, and 2) the method of statistical distance of probability distributions.
Fil: Bastos de Figueiredo, Julio Cesar. Escola Superior de Propaganda e Marketing; Brasil
Fil: Diambra, Luis Anibal. Universidad Nacional de La Plata. Centro Regional de Estudios Genómicos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Fil: Coraci Pereira, Malta. Universidade de Sao Paulo; Brasil