一类具时滞的超混沌系统的稳定性及控制分析

The stability and control analysis of a hyperchaos system with delay

研究一类新的超混沌系统的动力学性质,通过时滞反馈控制方法实现对该系统混沌控制的目的。分析具时滞的超混沌系统的平衡点的稳定性和Hopf分支的存在性,利用多时间尺度方法推导出具时滞超混沌系统Hopf分支的规范型,对极坐标下的规范型给出判断Hopf分支方向及分支周期解稳定性的判别准则,从理论上实现将混沌系统控制成为稳定状态。数值仿真结果验证了理论分析的正确性。

We study the dynamic behaviors of a new hyperchaos system. The aim of chaos control can be achieved by using delayed feedback control. We analyze the stability of the equilibrium and the existence of the Hopf bifurcation of the new system with delayed feedback. Furthermore, we deduce the normal form of Hopf bifurcation by using the multiple time scales method and investigate the criterion associated with the direction of Hopf bifurcation and the stability of periodic solution with the normal forms of polar coordinate. The hyperchaos system is controlled to be stable state in theory. Numerical examples are given to verify the theoretical results.