IDENTIFYING PHASE SYNCHRONOUS REGIMES IN NON-COHERENT AND MULTIPLE SCROLL ATTRACTOR SYSTEMS

Abstract

This work discusses the applicability of a method for phase determination of scalar time series from nonlinear systems. We apply the method to detect phase synchronization in different scenarios, and use the phase diffusion coefficient, the Lyapunov spectrum, and the similarity function to characterize synchronization transition in nonidentical coupled Rössler oscillators, both in coherent and non-coherent regimes. We also apply the method to detect phase synchronous regimes in systems with multiple scroll attractors as well as in experimental time series from coupled Chua circuits. The method is of easy implementation, requires no attractor reconstruction, and is particularly convenient in the case of experimental setups with a single time series data output.