Causality information planes and the characterization of chaotic dynamical systems

OSVALDO A. ROSSO; FELIPE OLIVARES; LUCIANO ZUNINO; LUCIANA DE MICCO; ANDRÉ L. L. AQUINO; ÁNGEL PLASTINO; HILDA A. LARRONDO

Santiago de Chile

Conferencia; XVII Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics (MEDYFINOL 2012); 2012

Facultad de Ingeniería y Ciencias Aplicadas de la Universidad de los Andes, Santiago de Chile, Chile

By appealing to a long list of different nonlinear maps and flows we exhaustively review the characterization of time series arising from these chaotic dynamical systems. The main tool for this characterization is the permutation Bandt-Pompe probability distribution function. We focus attention on both local and global characteristics of the components of this probability distribution function. The system´s localization in a causality entropy-complexity plane (global quantifier) and in a causality Shannon-Fisher plane (global vs local quantifier) displays typical specific features associated with its dynamics´ nature. We conclude that a good distinction between deterministic and stochastic dynamics is achieved via the present time series´ treatment based on the global characteristics of the permutation Bandt-Pompe probability distribution function for the evaluation of these two causality information planes.