| 一类平面多项式系统极限环的存在唯一性 |
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| 引用本文： | 刘兴国,黄立宏. 一类平面多项式系统极限环的存在唯一性[J]. 高校应用数学学报(A辑), 2007, 22(4): 455-461 |
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| 作者姓名： | 刘兴国 黄立宏 |
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| 作者单位： | 湖南工业大学,信息与计算科学系,湖南株洲,412008;湖南大学,数学与计量经济学院,湖南长沙,410082;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(10371034)，博士点基金(20050532023) |
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| 摘 要： | 研究一类平面2n 1次多项式微分系统的极限环问题,利用Hopf分枝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Cherkas和Zheilevych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： | 多项式系统 极限环 存在性 唯一性 |
| 文章编号： | 1000-4424（2007）04-0455-07 |
| 收稿时间： | 2006-12-23 |
Existence and uniqueness of limit cycle for a class of planar polynomial system |
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| LIU Xing-guo,HUANG Li-hong. Existence and uniqueness of limit cycle for a class of planar polynomial system[J]. Applied Mathematics A Journal of Chinese Universities, 2007, 22(4): 455-461 |
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| Authors: | LIU Xing-guo HUANG Li-hong |
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| Affiliation: | 1. Dept. of Inform. and Comput. Sci., Hunan Univ. of Tech., Zhuzhou 412008, China; 2. College of Mathematics and Econometrics, Hunan University, Changsha 410082, China |
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| Abstract: | The limit cycle problem for a class of planar polynomial differential system is studied. By using the theory of Hopf bifurcation,some sufficient conditions for the existence and stability of limit cycles of such systems are obtained.Furthermore,by applying Cherkas and Zheilevych's theorem about uniqueness,some sufficient conditions for the uniqueness of limit cycles of such systems are established. |
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| Keywords: | polynomial system limit cycle existence uniqueness |
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