Transition from Anticipatory to Lag Synchronization via Complete Synchronization
In this chapter we will consider chaos synchronization of two single scalar piecewise-linear time-delay systems studied in Chaps. 3 and 7 with unidirectional coupling between them and having two different time-delays: one in the coupling term and the other in the individual systems, namely feedback delay. We deduce  the corresponding stability condition for synchronization following Krasovskii-Lyapunov theory as in the previous chapter for complete synchronization, and demonstrate that there exist transitions between three different kinds of direct, and their inverse synchronizations, namely anticipatory, complete and lag synchronizations, as a function of the time-delay parameter in the coupling.
KeywordsDrive System Feedback Delay Complete Synchronization Feedback Delay Time Coupling Delay
- 20.M. Le Berre, E. Ressayre, A. Tallet, H.M. Gibbs, D.L. Kaplan, M.H. Rose, Phys. Rev. A 35, 3020 (1987)Google Scholar