Phase Synchronization in Unidirectionally Coupled Ikeda Time-delay Systems

TL;DR

This paper investigates phase synchronization in unidirectionally coupled Ikeda time-delay systems with hyperchaotic attractors, identifying a transition from approximate to phase synchronization without generalized synchronization.

Contribution

It demonstrates the existence of phase synchronization in complex hyperchaotic Ikeda systems and characterizes the transition using recurrence-based indices and Lyapunov exponents.

Findings

Phase synchronization occurs within a specific coupling range.

Approximate phase synchronization precedes exact phase synchronization.

Generalized synchronization does not occur in studied parameter ranges.

Abstract

Phase synchronization in unidirectionally coupled Ikeda time-delay systems exhibiting non-phase-coherent hyperchaotic attractors of complex topology with highly interwoven trajectories is studied. It is shown that in this set of coupled systems phase synchronization (PS) does exist in a range of the coupling strength which is preceded by a transition regime (approximate PS) and a nonsynchronous regime. However, exact generalized synchronization does not seem to occur in the coupled Ikeda systems (for the range of parameters we have studied) even for large coupling strength, in contrast to our earlier studies in coupled piecewise-linear and Mackey-Glass systems \cite{dvskml2006,dvskml2008}. The above transitions are characterized in terms of recurrence based indices, namely generalized autocorrelation function $P(t)$, correlation of probability of recurrence (CPR), joint probability of recurrence (JPR) and similarity of probability of recurrence (SPR). The existence of phase synchronization is also further confirmed by typical transitions in the Lyapunov exponents of the coupled Ikeda time-delay systems and also using the concept of localized sets.