| 基于Washout滤波器的Van der Pol-Duffing系统的Hopf分岔控制 |
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| 引用本文： | 杜文举,张建刚,俞建宁,安新磊.基于Washout滤波器的Van der Pol-Duffing系统的Hopf分岔控制[J].吉林大学学报(理学版),2014,52(3):568-574. |
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| 作者姓名： | 杜文举 张建刚 俞建宁 安新磊 |
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| 作者单位： | 兰州交通大学 数学系, 兰州 730070 |
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| 基金项目： | 国家自然科学基金(批准号:11161027;61364001);教育部科技研究重点项目(批准号:212180) |
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| 摘 要： | 对一类Van der Pol Duffing系统进行Hopf分岔分析, 并基于Washout滤波器设计状态反馈控制器, 讨论控制增益对Hopf分岔的存在性及其极限环幅值的影响. 结果表明, 选取适当的控制增益可以控制Hopf分岔的发生并改变极限环幅值的大小.
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| 关 键 词： | Hopf分岔 Washout滤波器 极限环幅值 分岔控制 |
| 收稿时间： | 2013-06-13 |
Control of Hopf Bifurcation in a Van der Pol Duffing-System Based on Washout Filter |
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| DU Wenju,ZHANG Jiangang,YU Jianning,AN Xinlei.Control of Hopf Bifurcation in a Van der Pol Duffing-System Based on Washout Filter[J].Journal of Jilin University: Sci Ed,2014,52(3):568-574. |
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| Authors: | DU Wenju ZHANG Jiangang YU Jianning AN Xinlei |
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| Institution: | Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China |
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| Abstract: | We studied the Hopf bifurcation and Hopf bifurcation control for a Van der Pol Duffing system. First of all, we analyzed the Hopf bifurcation and designed the linear and nonlinear state feedback controller for the autonomous system. Then, we designed a state feedback controller based on Washout filter, and discussed the impact of the control gain on the existence of the Hopf bifurcation and the limit cycle amplitude. Results show that selecting appropriate control gain can not only control the occurrence of Hopf bifurcation, but also change the size of the limit cycle amplitude. |
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| Keywords: | Hopf bifurcation Washout filter limit cycle amplitude bifurcation control |
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