Detecting phase synchronization in chaotic non-coherent Rössler systems using Discrete Complex Wavelet Approach (DCWA): preliminaries results

Abstract

Phase synchronization in non-identical coupled chaotic systems appears for some conditions in which weak coupling causes the systems time evolution to lock in phase to one another, while their amplitudes remain chaotic and uncorrelated. To identify his phenomenon, given a signal it is necessary to measure properly its phase. In this work, we applying our Discrete Complex Wavelet Approach (DCWA) for phase assignment, with aim to analyse two coupled chaotic Rössler systems in non-phase coherent regime. Our DCWA is based on the Dual-Tree Complex Wavelet Transform (DT–CWT), which is a form of a discrete wavelet transform that generates complex coefficient by using a dual-tree wavelet filters to obtain their real and imaginary parts. Due to its multi-scale properties in the context of phase characterization, it is possible to obtain very good results from scalar time series, even with chaotic systems.