| 一类非自治时滞反馈系统的分岔控制 |
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| 引用本文： | 钱长照,唐驾时.一类非自治时滞反馈系统的分岔控制[J].物理学报,2006,55(2):617-621. |
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| 作者姓名： | 钱长照 唐驾时 |
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| 作者单位： | (1)湖南大学工程力学系，长沙 410082; (2)湖南大学工程力学系，长沙 410082;长沙理工大学桥梁与结构工程学院，长沙 410076 |
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| 摘 要： | 对含有两个时滞参数、受简谐激励作用下的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主共振的分岔响应控制.首先采用摄动法从理论上推导出时滞动力系统的分岔响应方程，用奇异性理论得到了退化余维一分岔和余维二分岔的条件，以及Hopf分岔的存在性及发生该分岔的条件，最后用数值模拟的方法研究了时滞参数对系统分岔响应的影响.研究结果表明，适当选取时滞参数，不仅可以改变分岔响应曲线的拓扑形态， 还可以改变分岔点的位置.
关键词：
摄动法
分岔控制
时滞动力系统
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| 关 键 词： | 摄动法 分岔控制 时滞动力系统 |
| 文章编号： | 1000-3290/2006/55(02)/0617-05 |
| 收稿时间： | 03 31 2005 12:00AM |
| 修稿时间： | 6/1/2005 12:00:00 AM |
Bifurcation control for a non-autonomous system with two time delays |
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| Qian Chang-Zhao,Tang Jia-Shi.Bifurcation control for a non-autonomous system with two time delays[J].Acta Physica Sinica,2006,55(2):617-621. |
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| Authors: | Qian Chang-Zhao Tang Jia-Shi |
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| Institution: | 1. Department of Mechanics, Hunan University, Changsha 410082, China;2. College of Bridge and Structure Eginecring , Chongsha University of Soience and Technology, Changsha 410076, China |
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| Abstract: | A forced system with two time-delays, including van der Pol-Duffing types, is studied. The aim is to study the primary parametrical resonance bifurcation of this system. Perturbation method is used to obtain the bifurcation equation with time-delays. Based on the bifurcation equation, co-dimension one, co-dimension two and Hope bifurcation are discussed, and the effect of time-delays on the steady state response is analyzed by numerical methods. It is indicated that the primary resonance bifurcation can be well controlled by time-delays feedback. |
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| Keywords: | perturbation method bifurcation control dynamics of nonlinear systems involving time delays |
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