| 一类平面微分系统的极限环 |
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| 引用本文： | 刘兴国,黄立宏,吕勇.一类平面微分系统的极限环[J].大学数学,2009,25(3). |
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| 作者姓名： | 刘兴国 黄立宏 吕勇 |
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| 作者单位： | 1. 湖南工业大学,信息与计算科学系,湖南,株洲,412008
2. 湖南大学,数学与计量经济学院,湖南,长沙,410082 |
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| 基金项目： | 国家自然科学基金，博士点基金，湖南教育厅项目 |
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| 摘 要： | 研究一类平面微分系统的极限环,利用Hopf分支理论得到了该系统极限环存在性与稳定性的若干充分条件,利用ЧеркасЛА和ЖилевычЛИ的唯一性定理得到了极限环唯一性的若干充分条件.
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| 关 键 词： | 微分系统 极限环 唯一性 Hopf分支 |
Limit Cycles in a Class of Planar Differential System |
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| LIU Xing-guo,HUANG Li-hong,LV Yong.Limit Cycles in a Class of Planar Differential System[J].College Mathematics,2009,25(3). |
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| Authors: | LIU Xing-guo HUANG Li-hong LV Yong |
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| Institution: | 1.Department of Information and Computing Science;Hunan University of Technology;Zhuzhou 412008;China;2.College of Mathematics and Econometrics;Hunan University;Changsha 410082;China |
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| Abstract: | We study a class of planar differential system.By Hopf bifurcation theory,some sufficient conditions for the existence and stability of limit cycles of such system are obtained.Furthermore,by using of the Л. А.Черкас and Л.И.Жилевыч's theorem about uniqueness,some sufficient conditions for the uniqueness of limit cycles of such systems are established. |
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| Keywords: | differential system limit cycle uniqueness Hopf bifurcation |
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