Dual-time and cascaded anticipation of chaos synchronization

Using an Ikeda model, which was introduced to describe the dynamics of an optical bistable resonator it is demonstrated analytically that anticipating synchronization can be obtained in chaotic time-delay systems governed by two characteristic delay times. We derive existence and stability conditions for the dual-time anticipating synchronization manifold. We. also show that increased anticipation times for chaotic time-delay systems with two characteristic delay times can be obtained by the use of cascaded systems. The theory is in excellent, agreement with numerical simulations. We also derive existence conditions for cascaded anticipating synchronization in external cavity semiconductor lasers.