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.

arXiv comment5 Figures 9 pages

References in corpus (5)

• Transition from anticipatory to lag synchronization via complete synchronization in time-delay systems
• Approximating the mapping between systems exhibiting generalized synchronization
• Characteristics of a Delayed System with Time-dependent Delay Time
• Chaos Synchronization of delayed systems in the presence of delay time modulation
• Bifurcations and Chaos in Time Delayed Piecewise Linear Dynamical Systems

Cited by in corpus (2)

• Phase synchronization in time-delay systems
• Transition from phase to generalized synchronization in time-delay systems