一类高维动力学系统的混沌预测同步实现方法研究

摘要

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 withinτseconds 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.%对于一类含有时间项的高维非线性动力学系统，提出了实现混沌预测同步的控制方法。在混沌同步的基础上，建立了派生系统及差别方程，从理论上证明了提出的方法能够实现对于原非线性系统的预测同步。对于耦合项进行了简化，为了实现长时间的预测，建立了多级同步系统来延长预测同步时间。对于Duffing系统，以及含反馈单摆系统在混沌状态下进行了仿真计算，证明了提出的方法是正确的与有效的。