一个新4维超混沌系统的行为特性及其同步

The Dynamic Properties and Adaptive Synchronization of a New Four-Dimensional Hyper-Chaotic System

提出了一个新的4维超混沌系统,并对该系统的基本动力学特性进行了深入研究,得到系统的Lyapunov维数,给出了系统的时域图、相图、最大Lyapunov指数谱及其分岔图,并用非线性反馈控制方法实现了该超混沌系统的同步.根据系统的稳定性理论,得到了非线性反馈控制器的结构和系统达到混沌同步时反馈控制增益的取值范围,数值模拟结果验证了该方法的正确性.

A new four-dimensional chaotic system is reported. Basic dynamic properties of the new system are investi- gated via Lyapunov dimension, Lyapunov exponent, bifurcation and Poincare diagrams. Using nonlinear feedback con- trol, a method of chaos synchronization between the hyperchaos system and its duplicate system is proposed. Based on the stability theory, the functions of the nonlinear feedback control are determined and the range of feedback gain is de- rived. The results of numerical simulations are provided to show the effectiveness of the proposed method.