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Existence of anticipatory, complete and lag synchronizations in time-delay systems

D. V. Senthilkumar·M. Lakshmanan
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Abstract

Existence of different kinds of synchronizations, namely anticipatory, complete and lag type synchronizations (both exact and approximate), are shown to be possible in time-delay coupled piecewise linear systems. We deduce stability condition for synchronization of such unidirectionally coupled systems following Krasovskii-Lyapunov theory. Transition from anticipatory to lag synchronization via complete synchronization as a function of coupling delay is discussed. The existence of exact synchronization is preceded by a region of approximate synchronization from desynchronized state as a function of a system parameter, whose value determines the stability condition for synchronization. The results are corroborated by the nature of similarity functions. A new type of oscillating synchronization that oscillates between anticipatory, complete and lag synchronization, is identified as a consequence of delay time modulation with suitable stability condition.

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D. V. Senthilkumar, M. Lakshmanan. 2005-10-13. Existence of anticipatory, complete and lag synchronizations in time-delay systems. https://doi.org/10.1088/1742-6596%2F23%2F1%2F031

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