Anticipated synchronization of chaos for a class of high dimensional dynamic systems

For a class of high dimensional nonautonomous dynamic systems, the control method to realize anticipated synchronization of chaos was presented. Based on chaos synchronization, the derived system and difference equation for anticipated synchronization were built. It was proved that the control method can make the response of the derived system be identical with that of the original system within τ seconds theoretically. Furthermore, the coupling terms were simplified. To make the anticipation time longer, the multi-layer derived systems were built and they were coupled each other. A Duffing system and a pendulum with feedback were simulated to validate the correctness and effectiveness of the proposed method.