Periodic phase synchronization in coupled chaotic oscillators

Abstract

We investigate the characteristics of temporal phase locking states observed in the route to phase synchronization. It is found that before phase synchronization there is a periodic phase synchronization state characterized by periodic appearance of temporal phase-locking state and that the state leads to local negativeness in one of the vanishing Lyapunov exponents. By taking a statistical measure, we present the evidences of the phenomenon in unidirectionally and mutually coupled chaotic oscillators, respectively. And it is qualitatively discussed that the phenomenon is described by a nonuniform oscillator model in the presence of noise.

Characterizing the phase synchronization transition of chaotic oscillators

“…The system of Eq. (1) is known to show the CPS transition as is increased [11,13]. The phase of drive (response) oscillator is introduced as the rotation angle φ d(r) (t) around the origin in the x d(r) -y d(r) plane and the phase difference θ (t) of the coupled system is defined as…”

High-Dimensional Chaotic and Attractor Systems

“…Application of the concept of PS in these areas sheds light on the analysis of non-stationary bivariate data coming from biological systems which was thought to be impossible in the conventional statistical approach. And this calls new attention to the PS phenomenon [KK00,KLR03].…”

“…In this section, following [KK00,KLR03], we study the characteristics of TPL states observed in the regime from non-synchronization to PS in coupled chaotic oscillators. We report that there exists a special locking regime in which a TPL state shows maximal periodicity, which phenomenon we would call periodic phase synchronization (PPS).…”

“…It is important to define an appropriate phase variable in order to study the TPL state more thoroughly. In this regard, several methods have been proposed methods of using linear interpolation at a Poincaré section [RPK96], phase-space projection [RPK96, ROH98], tracing of the center of rotation in phase-space [YL97], Hilbert transformation [RPK96], or wavelet transformation [KK00,KLR03]. Among these we take the method of phase-space projection onto the x 1 − y 1 and x 2 − y 2 planes with the geometrical relation θ 1,2 = arctan(y 1,2 /x 1,2 ), and get phase difference ϕ = θ 1 − θ 2 .…”

“…In order to study the characteristics of the locking length τ , we introduce a measure [KK00,KLR03]: P ( ) = var(τ )/ τ , which is the ratio between the average value of time lengths of TPL states and their standard deviation. In terminology of stochastic resonance, it can be interpreted as noise-to-signal ratio [PK97,Jun93].…”