摘要
考虑含参数激励的广义Van der Pol方程的Hopf分岔与控制问题。通过设计线性位移和速度时滞反馈控制器构造了受控系统,着重研究了控制器对该类参数激励系统的1/2亚谐共振的分岔响应控制。采用多尺度法从理论上推导出时滞动力系统的分岔响应方程,并进一步得到Hopf分岔的存在条件。通过数值模拟,验证了所设计的控制器不仅能控制极限环的幅值,也能控制Hopf分岔的产生。
Hopf bifurcation and controlling of a generalized Van der Pol equation with parameter excitation are studied .The delayed feedback controller of linear displacement and velocity is designed to control the system .The paper is devoted to the study of the bifurcation response controlling of 1/2 harmonic resonance of the system .Bifurcation response equation of the time-delays dynamic system is obtained in theory by multiple scale method .Moreover , condition of the existence of Hopf bifurca-tion is also obtained .Numerical simulations show that the controller can control the bifurcation as well as the amplitude of limit cycle.
出处
《湖北师范学院学报（自然科学版）》
2013年第4期14-18,共5页
Journal of Hubei Normal University(Natural Science)
基金
国家自然科学基金资助项目(11172093
11032004)
湖南省研究生创新项目(CX2012B159)
关键词
HOPF分岔
极限环
时滞反馈控制
多尺度法
Hopf bifurcation
limit cycle
delayed feedback controller
multiple scale method
