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Phase synchronization in time-delay systems

D. V. Senthilkumar·M. Lakshmanan·J. Kurths
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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.

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D. V. Senthilkumar, M. Lakshmanan, J. Kurths. 2006-09-15. Phase synchronization in time-delay systems. https://doi.org/10.1103/physreve.74.035205

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