Exact anticipating synchronization in bi-directionally coupled time-delayed systems

We present an analytical investigation of exact anticipating synchronization between two bi-idirectionally coupled time-delayed systems in the case when these systems are governed by two characteristic times: the delay time in the coupling and the delay time in the coupled systems. We apply our approach to interpret the results of recent first experimental observation of anticipating chaos synchronization in external cavity semiconductor lasers with optical feedback.We establish that our approach can explain the experimental results only for special cases.