Existence of anticipatory, complete and lag synchronizations in time-delay systems
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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Cite
@article{arxiv.nlin/0510027,
title = {Existence of anticipatory, complete and lag synchronizations in time-delay systems},
author = {D. V. Senthilkumar and M. Lakshmanan},
journal= {arXiv preprint arXiv:nlin/0510027},
year = {2009}
}
Comments
5 Figures 9 pages