一个类Lorenz混沌系统Hopf分岔反控制

Anti-control of Hopf bifuraction for a Lorenz-like chaotic system

对混沌系统进行反控制可以实现分岔提前或者延迟发生,满足工程实际需要。以一个类Lorenz混沌系统为研究对象,根据Routh-Hurwitz准则和高维Hopf分岔理论,分析了系统Hopf分岔特性;提出了一种动态状态反馈控制法,对系统进行Hopf分岔反控制。通过调控控制参数,可以在预定任意位置产生Hopf分岔,使Hopf分岔提前或延迟发生,达到了预期的反控制目的。从分析结果看出,提出的动态状态反馈控制法可以避免复杂的计算过程,能够有效地实现对混沌系统的Hopf分岔反控制。

The anti-control of the chaotic system can achieve the advance or delay of the occurrence of bifurcation,which will meet the requirements of practical problems.In this paper,the Hopf bifurcation characteristics of a Lorenz-like chaotic system are analyzed based on the Routh-Hurwitz criterion and the high-dimensional Hopf bifurcation theory.A dynamic state feedback control law is proposed and applied to the anti-control of Hopf bifurcation.By tunning the value of the parameters,Hopf bifurcation can occur at any preset position,advancing or delaying the occurrence of Hopf bifurcation.The anti-control of Hopf bifurcation for the system is thus realized.The analysis results show that the dynamic state feedback control law can achieve the anti-control of Hopf bifurcation for the chaotic system with avoiding the complicated calculation process.