Global phase synchronization in an array of time-delay systems

TL;DR

This paper demonstrates the occurrence of global phase synchronization in an array of coupled Mackey-Glass time-delay systems with complex chaotic attractors, using multiple analytical approaches to confirm the synchronization process.

Contribution

It reveals the mechanism of sequential synchronization and cluster formation in a linear array of non-phase-coherent chaotic time-delay systems, validated by various phase and recurrence analysis methods.

Findings

Global phase synchronization achieved through sequential synchronization.

Clusters form before full synchronization as coupling strength increases.

Multiple analytical methods confirm the synchronization process.

Abstract

We report the identification of global phase synchronization (GPS) in a linear array of unidirectionally coupled Mackey-Glass time-delay systems exhibiting highly non-phase-coherent chaotic attractors with complex topological structure. In particular, we show that the dynamical organization of all the coupled time-delay systems in the array to form GPS is achieved by sequential synchronization as a function of the coupling strength. Further, the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster. We have confirmed these results by estimating instantaneous phases including phase difference, average phase, average frequency, frequency ratio and their differences from suitably transformed phase coherent attractors after using a nonlinear transformation of the original non-phase-coherent attractors. The results are further corroborated using two other independent approaches based on recurrence analysis and the concept of localized sets from the original non-phase-coherent attractors directly without explicitly introducing the measure of phase.