华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (5): 84-90.

• 应用数学与基础数学 • 上一篇    下一篇

达布多项式和二次系统周期解的存在性

邓桂丰   

  1. 上海立信会计学院 数学与信息学院, 上海 201620
  • 收稿日期:2010-02-01 修回日期:2010-06-01 出版日期:2010-09-25 发布日期:2010-09-25
  • 通讯作者: 邓桂丰

Existence of Darboux polynomial and periodic orbit of a quadratic system

DENG Gui-feng   

  1. School of Mathematics and Information, Shanghai Lixin University of Commerce, Shanghai 201620, China
  • Received:2010-02-01 Revised:2010-06-01 Online:2010-09-25 Published:2010-09-25
  • Contact: DENG Gui-feng

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摘要： 给出了平面高次系统具有不变实不可约达布多项式的充要条件. 在此基础上利用代数方法, 根据平面二次系统表达式中的二次多项式来判定系统平衡点是否有闭轨线环绕, 进而指出闭轨线内部的平衡点必须具备的一些条件.

关键词: 不可约达布多项式, 不变代数曲线, 平面二次系统, 周期解, 不可约达布多项式, 不变代数曲线, 平面二次系统, 周期解

Abstract: This paper derived the necessary and sufficient condition for the existence of invariant real irreducible algebraic curve of a polynomial differential system. Using this result and quadratic polynomials of quadratic system, we established some criteria to determine whether equilibrium was circled by a closed orbit. Finally, a property of the equilibrium enclosed in a periodic orbit
was deduced for quadratic system.

Key words: invariant algebraic curve, quadratic differential system, periodic orbit, irreducible Darboux polynomial, invariant algebraic curve, quadratic differential system, periodic orbit

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