| 三次系统极限环的分支研究 |
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| 引用本文： | 应益荣,吴冲锋.三次系统极限环的分支研究[J].天津师范大学学报(自然科学版),2001,21(4):20-23. |
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| 作者姓名： | 应益荣 吴冲锋 |
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| 作者单位： | 上海交通大学管理学院, |
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| 基金项目： | 国家杰出青年自然科学基金资助项目(70025303) |
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| 摘 要： | 从微分方程一般理论出发，研究了平面三次多项式系统在原点周围和赤道附近同时产生极限环分支的情形。通过改变位于原点的奇点的稳定性，结合分析三次系统向量场在无穷远处的分支，得到了恰有一个无穷远奇点的三次系统分别在原点周围和赤道附近同时存在多个极限环的充分条件。
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| 关 键 词： | 极限环 Hopf分支 三次系统 微分方程 |
| 文章编号： | 1671-1114(2001)04-0020-04 |
| 修稿时间： | 2001年5月22日 |
Study on Distribution
of Limit Cycles of Cubic Systems |
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| YING Yi-rong,Wu Chong-feng.Study on Distribution
of Limit Cycles of Cubic Systems[J].Journal of Tianjin Normal University(Natural Science Edition),2001,21(4):20-23. |
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| Authors: | YING Yi-rong Wu Chong-feng |
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| Abstract: | Start with the general theory and then specialized to the particular case of cubic polynomial systems for which the simultaneous bifurcation of limit cycles from the origin and the equator is studied. By means of method of changing the stability of singular at the origin, combining with the method of researching the bifurcation at infinity in vector fields of cubic system, the sufficient conditions for the existence of several limit cycles around the origin or near the equator respectively to a class of cubic system which has exactly an unique singular point at infinity are obtained. |
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| Keywords: | limit cycle Hopf bifurcation cubic system |
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