Henon系统的混沌控制研究

The study of controlling chaos of the Henon system

运用数值仿真的方法,研究了三种控制Henon系统系统混沌的方法,并比较了这三种方法的适应性和控制效果。通过Henon系统在混沌状态下的吸引子、吸引盆、分岔图及其对应的最大Lyapunov指数谱,揭示了Henon系统系统通向混沌的途径。利用数值运算,得到系统的不稳定的周期1和不稳定周期2轨道。通过非线性反馈控制方法、间歇反馈方法和压缩相空间控制法,对系统进行了控制。结果表明,这3种控制方法都可以有效地将Henon系统的混沌状态控制到稳定的周期轨道。

In this paper, three methods which controlled the chaos of the Henon system were studied and compared the efficiency of these methods. At first, the attractor, the basin of Henon,the spectra of the Max Lyapunov exponents, the spectra of the Lyapunov exponent and the bifurcation diagram through computer simulation were got.Then the unstable fixed points and the two-periodic of the system were got by numerical compute. The chaos of the Henon system was controlled by means of the methods of nonlinear feedback, intermittent nonlinear feedback and compressing phrase space. The result indicated that the chaotic motions of the system can be successfully converted to the stable periodic orbits after the three methods were used to control chaos.