| 具有25阶奇点的一类5次多项式微分系统的结构 |
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| 引用本文： | 孙莹,李学敏.具有25阶奇点的一类5次多项式微分系统的结构[J].华东师范大学学报(自然科学版),2005,2005(1):9-15,39. |
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| 作者姓名： | 孙莹 李学敏 |
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| 作者单位： | 华东师范大学,数学系,上海,200062;山东师范大学,数学系,山东,济南,250014 |
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| 摘 要： | 研究在第一临界情形下的一类特殊的5次多项式微分系统，利用Poincaré变换、环域定理、闭轨道星形的特点等方法，得到有关极限环的存在性、唯一性及稳定性的结果；指出第一临界情形下的一类5次系统，至多有一个极限环，如果存在则是稳定的.并给出了存在性条件，进而指出了其所有可能的全局相图，计有64种.
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| 关 键 词： | 高阶奇点 有限远奇点 无穷远奇点 临界情形 |
| 文章编号： | 1000-5641(2005)01-0009-07 |
| 收稿时间： | 2003-12-1 |
| 修稿时间： | 2004-3-5 |
The Structure of a Class of Polynomial Differential Systems of Degree 5 with a 25th order Singularity(Chinese) |
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| SUN Ying,LI Xue-min.The Structure of a Class of Polynomial Differential Systems of Degree 5 with a 25th order Singularity(Chinese)[J].Journal of East China Normal University(Natural Science),2005,2005(1):9-15,39. |
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| Authors: | SUN Ying LI Xue-min |
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| Institution: | 1. Department of Mathematics, East China Normal University, Shanghai 200062, China;2. Department of Mathematics, Shandong Normal University, Jinan 250014, China |
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| Abstract: | Using Poincare transformation and Poincare-Bendixson theorem, sufficient conditions for the existence, uniqueness and stability of the limit cycles for a kind of fifth order differential equation are obtained. It is proved that such a kind of systems has at most one limit cycle and the existence is accompanied by the stability. Furthermore, almost all possible global phase portraits, 64 altogether, are indicated. |
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| Keywords: | higher order singular point finite singular point infinite singular point critical conditon |
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