三维类Lorenz混沌系统的变形与超混沌实现

Reforming of One Class of Lorenz-like System and Hyperchaos Realization

在三维类Lorenz混沌系统的基础上增加一维状态和两个参数,构建了一个新的四维超混沌系统。利用非线性动力学分析方法简要分析了该系统平衡点的稳定性、超混沌吸引子的相图、分岔图、Lyapunov指数谱和Lyapunov维数等基本动力学特性。结果发现新的四维系统随着新引入的两个参数(p和m,pu为非线性控制器,u的变化率u=mx)变化分别呈现周期、拟周期、混沌及超沌混动力学行为,动力学行为相同,但随m的变化范围较大。

The new four-dimensional hyperchaos system was built by adding an additional state and two parameters into the three-order Lorenz-like system. Its basic dynamical properties were studied briefly, such as the stability of equilibrium, the hyperchaos attractor, bifurcation diagram, Lyapunov exponent spectrum and fractal dimension by nonlinear techniques. The results show that the new system＇ s dynamics behavior can be periodic, quasi-periodic, chaotic and hyperchaotic as the new introduced two parameters （ p and ra , pu is the nonlinlear controller, the variance ratio of u is u ·=mx ） vary respectively and have greater variation with m.