【摘要】 运用多尺度法研究了一类van der Pol-Duffing系统的Hopf分岔问题和分岔控制问题.首先,分析了自治的van der Pol-Duffin g系统的Hopf分岔问题,并设计了线性和非线性联合的状态反馈控制器,对其进行了Hopf分岔控制.然后,设计了线性时滞参数,对非自治时滞反馈系统的主共振分岔响应进行了控制.研究结果表明,适当选取参数不仅可以改变分岔响应曲线的拓扑形态,还可以改变分岔点的位置.更多还原

【Abstract】 We study the Hopf bifurcation and the Hopf bifurcation control of a van der Pol-Duffing system by the method of multiple scales.Firstly,we investigated the Hopf bifurcation of the autonomous van der system and designed a linear and nonlinear state feedback controller to control the Hopf bifurcation.Then, the linear time delay parameter is designed and the primary resonance bifurcation response control of a non-autonomous feedback system is investigated in detail.Results show that the primary resonance bifurcation can be well controlled by the time-delays feedback control if theparameters is appeopriate.更多还原