Phase synchronization in time-delay systems

Abstract

Though the notion of phase synchronization has been well studied in chaotic dynamical systems without delay, it has not been realized yet in chaotic time-delay systems exhibiting non-phase coherent hyperchaotic attractors. In this article we report the first identification of phase synchronization in coupled time-delay systems exhibiting hyperchaotic attractor. We show that there is a transition from non-synchronized behavior to phase and then to generalized synchronization as a function of coupling strength. These transitions are characterized by recurrence quantification analysis, by phase differences based on a new transformation of the attractors and also by the changes in the Lyapunov exponents. We have found these transitions in coupled piece-wise linear and in Mackey-Glass time-delay systems.

4 pages, 3 Figures (To appear in Physical Review E Rapid Communication)

References in corpus (5)

• Anticipated synchronization in coupled inertia ratchets with time-delayed feedback: a numerical study
• Transition from anticipatory to lag synchronization via complete synchronization in time-delay systems
• Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers
• Bifurcations and Chaos in Time Delayed Piecewise Linear Dynamical Systems
• Existence of anticipatory, complete and lag synchronizations in time-delay systems

Cited by in corpus (14)

• How to avoid potential pitfalls in recurrence plot based data analysis
• Transition from phase to generalized synchronization in time-delay systems
• Synchronization in hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment
• Stability of synchronization in coupled time-delay systems using Krasovskii-Lyapunov theory
• Experimental confirmation of chaotic phase synchronization in coupled time-delayed electronic circuits
• Global phase synchronization in an array of time-delay systems
• Inverse synchronizations in coupled time-delay systems with inhibitory coupling
• Intermittency transition to generalized synchronization in coupled time-delay systems
• Dynamic environment coupling induce synchronized states in coupled time-delayed electronic circuits
• Global generalized synchronization in networks of different time-delay systems
• Phase Synchronization in Unidirectionally Coupled Ikeda Time-delay Systems
• Zero-lag synchronization in coupled time-delayed piecewise linear electronic circuits
• Global and Partial Phase Synchronizations in Arrays of Piecewise Linear Time-Delay Systems
• Deterministic transport of particles in a micro-pump