Analysis of phase synchronization of coupled chaotic oscillators with empirical mode decomposition

Abstract

Empirical mode decomposition is investigated as a tool to determine the phase and frequency and to study phase synchronization between complex chaotic oscillators. Within this approach, the oscillator is characterized by a spectrum of frequencies corresponding to the empirical modes. First, the phase and frequency of the oscillators resulting from two well-known methods, based on modified variables and the Poincaré surface of section, are compared with those obtained using empirical mode decomposition. Next, for both parametrically and essentially different chaotic oscillators coupled as a drive-response system, transition to phase synchronization between corresponding empirical modes is investigated, defined as an adjustment of the mode frequencies of the response oscillator to those of the drive oscillator as the coupling is increased. In particular, anomalous and imperfect phase synchronization between modes is observed.