| 引用本文: | 钱长照,李克安.一类非线性动力系统的时滞反馈分叉控制.[J].国防科技大学学报,2005,27(5):82-85.[点击复制] |
| QIAN Changzhao,LI Kean.Bifurcation Controlling of a Nonlinear Dynamics System with Time-dalays Feedback[J].Journal of National University of Defense Technology,2005,27(5):82-85[点击复制] |
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| 一类非线性动力系统的时滞反馈分叉控制 |
| 钱长照1, 李克安2 |
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(1.湖南大学 工程力学系，湖南 长沙 410082;2.湖南理工学院，湖南 岳阳 411400)
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| 摘要: |
| 对时滞控制作用下的参数激励van der Pol-Duffing方程进行了研究，着重研究了时滞参数对该类参数激励系统的1/2亚谐共振－主参数共振分叉响应控制。首先采用摄动法从理论上推导出时滞动力系统的分叉响应方程，再采用数值模拟的方法研究了时滞参数对系统分叉响应的影响。研究结果表明，适当选取时滞参数，不仅可以改变分叉响应曲线的拓扑形态，还可以平移分叉响应曲线，即使其分叉提前或滞后，还能同时满足这两种要求。 |
| 关键词: 摄动法 分叉控制 时滞动力系统 |
| DOI： |
| 投稿日期：2005-04-19 |
| 基金项目:国家自然科学基金资助项目(10472029) |
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| Bifurcation Controlling of a Nonlinear Dynamics System with Time-dalays Feedback |
| QIAN Changzhao1, LI Kean2 |
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(1.Department of Engineering Mechanics，Hunan University, Changsha 410082，China;2.Hunan Institute of Science and Technology, Yueyang 411400，China)
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| Abstract: |
| The van der Pol-Duffing equation, excited under the parameters with two time delays, is studied. The main aim is to study 1/2 subharmonic-primary parametrical resonance bifurcation of this system. Perturbation method is used to obtain the bifurcation equation with time-delays, and numerical method is utilized to analyze the effect of time-delays on the steady state response. The research indicates that 1/2 subharmonic-primary parametrical resonance bifurcation can be well controlled by time-delays feedback. |
| Keywords: perturbation method bifurcation controlling dynamics of nonlinear systems involving time dealys |
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