数学物理学报 ›› 2022, Vol. 42 ›› Issue (2): 353-364.

• 论文 • 上一篇    下一篇

带两条平行切换直线多项式微分系统的极限环分支

姜雪丽,邓璇,文邱浩,熊艳琴*()   

  1. 南京信息工程大学数学与统计学院 南京 210044
  • 收稿日期:2021-08-12 出版日期:2022-04-26 发布日期:2022-04-18
  • 通讯作者: 熊艳琴 E-mail:yqxiong@nuist.edu.cn
  • 基金资助:
    国家自然科学基金(11701289)

Limit Circle Bifurcations of Polynomial Differential System with Two Parallel Switch Straight Lines

Xueli Jiang,Xuan Deng,Qiuhao Wen,Yanqin Xiong*()   

  1. School of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing 210044
  • Received:2021-08-12 Online:2022-04-26 Published:2022-04-18
  • Contact: Yanqin Xiong E-mail:yqxiong@nuist.edu.cn
  • Supported by:
    the NSFC(11701289)

摘要:

该文研究了一类带两条平行切换直线多项式微分系统的极限环分支问题. 借助广义首阶Melnikov函数及相关定性理论知识, 导出其代数结构及相应系数表达式, 再根据系数的相互变化研究广义双同宿分支, 获得其环性数的一个下界.

关键词: 不连续微分系统, 极限环, Melnikov函数, 同宿分支

Abstract:

In this paper, the limit cycle bifurcation problem is investigated for a class of polynomial differential system with two parallel switch straight lines. We use the generalized first order Melnikov function and related qualitative theory of knowledge to export the algebraic and corresponding coefficients of expression, then, use coefficient of change to research generalized double homoclinic bifurcation, and get a lower bound of its ring number.

Key words: Discontinuous planar system, Limit cycle, Melnikov function, Homoclinic bifurcations

中图分类号: 

  • O175.1