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 (2)

• Anticipated synchronization in coupled inertia ratchets with time-delayed feedback: a numerical study
• Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers

Cited by in corpus (3)

• Transition from phase to generalized synchronization in time-delay systems
• Intermittency transition to generalized synchronization in coupled time-delay systems
• Phase Synchronization in Unidirectionally Coupled Ikeda Time-delay Systems