Chen式系统的混沌控制

Chaos Control of Chen System

根据Chen式系统的动力学方程,利用四阶Runge-Kutta算法数值仿真了系统随自身参数变化的全局分岔图和混沌态时的相图和时间历程图。分别用自适应控制法及x |x|控制法对系统进行控制,对比了两种控制法对系统控制的结果,得到了自适应控制法能将系统控制在稳定周期轨道,周期运动经倍化分岔序列转变为混沌态后较稳定,而x|x|控制法控制系统,存在叉式分岔、倍化分岔,演变为混沌态后又转变为周期运动,且行为交替出现的丰富动力学行为的结论,提供了该系统混沌行为控制为周期行为的参数多区域选择,为该系统在实际工程应用中的混沌控制提供了理论支持,为其他系统的混沌控制提供了经验和方法。

This paper according to the dynamic equation of the Chen system, the global bifurcation diagram and phase diagram and time history diagram of the chaotic state which with parameter change of the system is numerical simulation algorithm of using fourth order Runge Kutta. The system is controlled by adaptive control method andx / x/ control method, the results of two control methods are compared, the conclusion is got that the adaptive control method can be used to control the system in a stable periodic orbit, the periodic motion transformed into a chaotic state of the doubling bifurcation that is relatively stable, but thex Ix I controlled system, having a fork type bifurcation, doubling bifurcation, evolutioning the chaotic state then transformation into the periodic movement, and the abundant dynamic behavior include that the dynamic behavior was alternately diverted, Provide parameters for multi area selection that the chaotic behavior of the system is controlled to periodic behavior, provided the theoretical support for the chaos control in the practical engineering application of this system, and provided the experience and methods for the chaos control of other systems.