Estimation of Dynamical Phase Models for Chaotic Oscillators
Leandro Freitas de Abreu Abreu1; Luis Antonio Aguirre Aguirre2
1 Instituto Federal de Minas Gerais Campus Betim; 2 Universidade Federal de Minas Gerais
Resumo
Despite the advances in synchronization theory, a complete understanding about the best coupling variable to synchronize chaotic oscillators, in a general way, is still lacking. Dealing with periodic oscillators, one of the most successful approaches is the phase description method, where a dynamical model is obtained to describe the evolution of the phase of the system. Conclusions about synchronous regimes of the system (e.g. Arnold tongues) can be estimated by analyzing only the phase model. This work presents an attempt to extend this approach to chaotic oscillators, by means of modelling its phase dynamics, based on the evolution of the states. Phase models for the Rössler and Lorenz systems were estimated from data using system identification techniques. The paper investigates the feasibility of choosing the most adequate variable for coupling oscillators by analyzing the phase model -- structure and parameters. This could lead to a more systematic way of investigating aspects of synchronizability.
Palavras-chave: Synchronization in Nonlinear Systems; Modeling, Numerical Simulation and Optimization; Control in Complex Systems