Global phase synchronization in an array of time-delay systems

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.

11 pages, 13 figures, Appear in Physical Review E

References in corpus (11)

• Recurrence Plots for the Analysis of Complex Systems
• Synchronization in complex networks
• Synchronization of Kuramoto Oscillators in Scale-Free Networks
• Experimental evidence for phase synchronization transitions in human cardio-respiratory system
• Phase synchronization in time-delay systems
• General Framework for phase synchronization through localized sets
• Transition from phase to generalized synchronization in time-delay systems
• Phase Synchronization in Temperature and Precipitation Records
• Spatial synchronization and extinction of species under external forcing
• Universal Critical Behavior of the Synchronization Transition in Delayed Chaotic Systems
• Phase Synchronization in Unidirectionally Coupled Ikeda Time-delay Systems

Cited by in corpus (5)

• Synchronization in hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment
• Experimental confirmation of chaotic phase synchronization in coupled time-delayed electronic circuits
• Geometric and dynamic perspectives on phase-coherent and noncoherent chaos
• Transition to complete synchronization and global intermittent synchronization in an array of time-delay systems
• Global and Partial Phase Synchronizations in Arrays of Piecewise Linear Time-Delay Systems