四维超混沌系统Hopf分岔分析与反控制

对超混沌系统进行分岔反控制的研究已成为当前一个重要研究方向，常采用线性控制器实现反控制。首先，对一个四维超混沌系统的Hopf分岔特性进行了分析，利用高维分岔理论推导出分岔特性与参数之间的关系式，以此判断系统的分岔类型。然后，设计一个由线性与非线性组合成的混合控制器对系统进行分岔反控制，控制参数取值不同时，系统会呈现出不同的分岔特性。通过分析得出，调控线性控制器参数可以使系统Hopf分岔提前或延迟发生；同时，调控混合控制器的两个控制参数，可以改变系统Hopf分岔特性，实现分岔反控制。

Hopf bifurcation analysis and anti-control of bifurcation of a four-dimensional hyperchaotic systems

Anti-control of bifurcation of hyperchaotic systems is a new field of nonlinear scientific research.It is often implement through a linear controller in most cases.In this paper,the Hopf bifurcation behaviors of a four-dimensional hyper chaotic system are studied,and the relationships between the bifurcation characteristics and parameters are obtained by using the high dimensional bifurcation theory,to determine the bifurcation type of the system.Then a combined linear and nonlinear controller is designed for anti-control of bifurcation.At different control parameter values,the systems exhibits different bifurcation characteristics.The results show that through changing the linear controller parameters,the system Hopf bifurcation can be moved forward or delayed.Through changing two controller parameters,Hopf bifurcation characteristics of the system can be modified to achieve anti-control of bifurcation.