一类混沌系统的Hopf分岔控制

针对带参数的混沌系统，运用 Routh-Hurwitz判据及 Hopf分岔理论研究系统存在的动力学行为，设计状态反馈控制器对系统进行 Hopf分岔控制。分析系统参数及控制参数分别对系统稳定性与 Hopf分岔类型的影响，得到了系统稳定及不发生 Hopf分岔的系统参数条件。研究结果表明：控制器中的线性控制部分及非线性控制部分均能改变系统的分岔行为，使系统渐近稳定。数值仿真证明控制器设计的有效性。

Hopf Bifurcation Control of a Chaotic System

Using Routh-Hurwitz criterion and hopf bifurcation theory, the dynamical behaviors of a chaotic system with parameters were investigated, and a feedback controller was designed to stabilize the system. The effects of the system parameters and controller parameters on the system stability and hopf bifurcation type were discussed, and the parameter conditions for the system stability with no hopf bifurcation were found out. The results indicate that both the linear control part and nonlinear control part in the controller can change the bifurcation behaviors of the system, which make the system asymptotically stable. Finally the numerical simulation proves the effectiveness of the controller.