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Isochronal synchronization of time delay and delay-coupled chaotic systems

This paper studies the problem of isochronal synchronization of time-delay chaotic systems featuring also coupling delay. Based on the Lyapunov–Krasovskii stability theory, sufficient conditions are derived for the stability of isochronal synchronization between a pair of identical chaotic systems. Such criteria permit the proper design of stable proportional linear feedback controller, more specifically, the design of adequate proportional feedback gain matrices. The proposed criteria are suited to systems with (i) intrinsic delay, (ii) coupling delay or (iii) both. Numerical simulations of the synchronization of delay-coupled systems are presented as examples of the application of the criteria.