一个新的四维超混沌系统的动力学分析及混沌反同步

Dynamical analysis and anti-synchronization for a new four dimensional hyperchaotic system

提出了一个新的四维Chen-Qi-like混沌系统。通过计算该系统的时间序列的Lyapunov指数谱、Lyapunov维数、分岔图、Poincaré截面图等分析了控制参数变化时,系统的非线性动力学特征。结果表明该新系统不但和Chen-Qi系统族有类似的性质,而且又呈现不同的非线性特征。在微分方程不变性原理基础上,运用LMI技术和Riccati方程,设计了一类新的非线性反馈控制器,实现了超混沌系统的反同步。仿真结果验证了该方法的可行性和有效性。

A new Chen-Qi-like four dimensional chaotic system is presented. The nonlinear characteristic of the new system versus the control parameters is illustrated by Lyapunov exponent, Lyapunov dimension, bifurcation diagrams and Poincare section etc. The results indicate that this new system has some similar characteristics to the Chen-Qi family, and presents some distinct nonlinear properties. A new nonlinear controller is designed based on the invariance principle of differential equations Riccati equations and LMI. With this method, the anti-synchronization of hyperchaotic systems can be achieved. Numerical simulation shows the feasibility and effectivenes of the proposed scheme.