华东师范大学学报(自然科学版) ›› 2005, Vol. 2005 ›› Issue (1): 9-15,3.

• 数学 统计学 • 上一篇    下一篇

具有25阶奇点的一类5次多项式微分系统的结构

孙莹1，李学敏2   

  1. 1. 华东师范大学 数学系，上海 200062; 2.山东师范大学 数学系, 山东济南 250014
  • 收稿日期:2003-12-01 修回日期:2004-03-05 出版日期:2005-03-25 发布日期:2005-03-25
  • 通讯作者: 孙莹

The Structure of a Class of Polynomial Differential Systems of Degree 5 with a 25th order Singularity(Chinese)

SUN Ying1 , LI Xue-min2   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200062, China;2. Department of Mathematics, Shandong Normal University, Jinan 250014, China
  • Received:2003-12-01 Revised:2004-03-05 Online:2005-03-25 Published:2005-03-25
  • Contact: SUN Ying

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.

关键词: 高阶奇点, 有限远奇点, 无穷远奇点, 临界情形, 高阶奇点, 有限远奇点, 无穷远奇点, 临界情形

Abstract: Using Poincaré transformation and Poincaré-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.

Key words: finite singular point, infinite singular point, critical conditon, higher order singular point, finite singular point, infinite singular point, critical conditon

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