一类van der Pol-Duffing系统的Hopf分岔控制  

Hopf Bifurcation Control of a van der Pol-Duffing System

作　　者：秦爽[1] 张建刚[1] 杜文举[2] 俞建宁[1] QIN Shuang ZHANG Jiangang DU Wenju YU Jianning(School of Mathematics and Physics, Lanzhou Jiaotong University, Gansu Lanzhou 730070, China School of Traffic and Transportation, Lanzhou Jiaotong University, Gansu Lanzhou 730070, China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070 [2]兰州交通大学交通运输学院,甘肃兰州730070

出　　处：《河北师范大学学报（自然科学版）》2017年第1期24-31,共8页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(61364001)

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.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.

关 键 词：HOPF分岔 多尺度法 反馈控制 时滞反馈系统 

分 类 号：O415[理学—理论物理]