参数激励下单向耦合的Lorenz系统广义同步复杂性

Complexity of Generalized Synchronization of Unidirectional Coupled Lorenz Systems under Parametric Excitation

针对响应系统具有参数周期扰动的情况,对两个单向耦合的Lorenz系统的广义同步(GS,generalized synchronization)问题进行了研究。基于稳定性理论和广义Hamilton函数理论,借助辅助系统方法和Melnikov方法,提出了修正系统进入混沌轨道和各种复杂周期轨道附近的充分条件,进而得到了参数激励下两个单向耦合的Lorenz系统达到广义同步的充分条件,说明了广义同步的复杂性结论.Matlab数值仿真实验证明了该方法的正确性与有效性。

A new method was investigated to the generalized synchronization （GS） of two unidirectional coupled Lorenz systems when the response system had parametric excitation. Based on stability theories and Hamilton theorem, the sufficient conditions were given to the modified system by methods of auxiliary-system and Melnikov when the modified system came to chaotic orbits and kinds of different periodic orbits, then, the existence of generalized synchronization of two unidirectional coupled Lorenz systems under parametric excitation was strictly proven. All of these have shown the conclusion that generalized synchronization is complicated. Finally, a numerical simulation illustrates the correctness and effectiveness of the present method.