一类多项式系统极限环惟一性与奇点分支

J4 ›› 2009, Vol. 44 ›› Issue (9): 90-92.

一类多项式系统极限环惟一性与奇点分支

张志戎

铜陵学院数学与计算机科学系, 安徽铜陵 244000

出版日期:2009-09-16 发布日期:2009-11-05
作者简介:张志戎(1968-),女,讲师,研究方向为应用微分方程. Email:zzrellen@163.com
基金资助:
安徽省教育厅重点基金资助项目(2005kj031ZD; 050460103)

The uniqueness of the limit cycle and the bifurcation of singular points for a class of polynomial systems

ZHANG Zhi-Reng

Department of Mathematics and Computer Science, Tongling University, Tongling 244000, Anhui, China

Online:2009-09-16 Published:2009-11-05

摘要/Abstract

摘要：

得到一类多项式系统dx/dt=-y+δx+lx²+mxy,dy/dt=x(1+a₁y+…+a_ny)在奇点O(0,0)的焦点量公式和极限环存在惟一性的完整结果,最后给出不变直线上各奇点的分支情况及几何特征。

关键词: 多项式系统;极限环;存在惟一性;分支

Abstract:

This paper gives complete results concerning the focus values at O(0,0), and the existence uniqueness of limit cycles for a class of polynomial systems dx/dt=-y+δx+lx²+mxy,dy/dt=x(1+a₁y+…+a_ny),Finally the geometric characteristics of singular points which lie on the invariant straight lines are given.

Key words: polynomial system; limit cycle; existence uniqueness;bifurcation

中图分类号:

O175.12

张志戎. 一类多项式系统极限环惟一性与奇点分支[J]. J4, 2009, 44(9): 90-92.

ZHANG Zhi-Reng. The uniqueness of the limit cycle and the bifurcation of singular points for a class of polynomial systems[J]. J4, 2009, 44(9): 90-92.

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