Anticipation in the synchronization of chaotic time-delay systems

We study numerically the synchronization of two time-delay chaotic systems, in a unidirectional coupling configuration. The coupling is delayed in time to represent the finite speed at which the information is transmitted from one system (master system) to the other (slave system). We simulate coupled Mackey–Glass and Ikeda systems. We show that, when the delay time of the systems, τ, is greater than the delay time of the coupling, τ2, for adequate parameters a regime of anticipated synchronization occurs. In this regime, the slave system at time t, synchronizes to the future state of the master system, at time t+τ−τ2, anticipating its chaotic evolution. Anticipation in the synchronization is not destroyed by small parameter differences between the systems, but in this case the systems are not perfectly synchronized.