| Liénard方程Poincaré分岔极限环的唯一性 |
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| 引用本文： | 岳喜顺.Liénard方程Poincaré分岔极限环的唯一性[J].数学学报,2005,48(2):377-384. |
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| 作者姓名： | 岳喜顺 |
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| 作者单位： | 华南理工大学自动化科学与工程学院 广州510640 |
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| 基金项目： | 国家自然科学基金资助项目(60004004,60475004)
华南理工大学科研启动基金资助项目 |
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| 摘 要： | 本文利用隐函数定理和一阶Mel'nikov函数,对Lienard方程Poincare分岔极 限环的唯一性进行了探讨, 同时也对闭轨的不存在性进行了分析,给出了若干判据. 通过对一阶Mel'nikov函数进行变形, 引入了新的判定函数, 由此得到了更为简单的 判定条件.
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| 关 键 词： | Liénard方程 Poincaré分岔 唯一性 |
The Uniqueness of Limit Cycles from Poincare Bifurcation of Lienard Equation |
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| Xi Shun YUE College of Automation Science and Engineering,South China University of Technology,Guangzhou ,P. R. China.The Uniqueness of Limit Cycles from Poincare Bifurcation of Lienard Equation[J].Acta Mathematica Sinica,2005,48(2):377-384. |
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| Authors: | Xi Shun YUE College of Automation Science and Engineering South China University of Technology Guangzhou P R China |
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| Institution: | Xi Shun YUE College of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, P. R. China |
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| Abstract: | This paper deals with the uniqueness of limit cycles from Poincare bifurcation of Lienard equation by usmg the implicit function theorem and the first order Mel'nikov function. Meanwhile, the case of non-existence of closed orbit is also investigated, some criteria are obtained. After modifying the first order Mel'nikov function, a new decision function is introduced, so the decision conditions become more simple. |
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| Keywords: | Lienard equation Poincare bifurcation Uniqueness |
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