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 tim e to represent the finite speed at which the information is transmitted fro m one system (master system) to the other (slave system). We simulate coupl ed Mackey-Glass and Ikeda systems. We show that, when the delay time of the systems, tau, is greater than the delay time of the coupling, tau (2), for adequate parameters a regime of anticipated synchronization occurs. In thi s regime, the slave system at time t, synchronizes to the future state of t he master system, at time t + tau -tau (2), anticipating its chaotic evolut ion. Anticipation in the synchronization is not destroyed by small paramete r differences between the systems, but in this case the systems are not per fectly synchronized. (C) 2001 Elsevier Science B.V. All rights reserved.