数学物理学报 ›› 2016, Vol. 36 ›› Issue (5): 919-927.

• 论文 • 上一篇    下一篇

一类二次等时微分系统在不连续二次多项式扰动下的极限环分支

李时敏1, 岑秀丽2   

  1. 1. 广东财经大学数学与统计学院 广州 510320;
    2. 清华大学数学科学系 北京 100084
  • 收稿日期:2015-12-24 修回日期:2016-06-12 出版日期:2016-10-26 发布日期:2016-10-26
  • 作者简介:李时敏,E-mail:lism1983@126.com;岑秀丽,E-mail:cenxiuli2010@163.com
  • 基金资助:

    国家自然科学基金(11401111,11171355)资助

Limit Cycles for Perturbing Quadratic Isochronous Center Inside Discontinuous Quadratic Polynomial Differential System

Li Shimin1, Cen Xiuli2   

  1. 1. School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou 510320;
    2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084
  • Received:2015-12-24 Revised:2016-06-12 Online:2016-10-26 Published:2016-10-26
  • Supported by:

    Supported by the NSFC (11401111, 11171355)

摘要:

该文研究了二次等时微分系统?=-y-(4)/(3)x2?=x-(16)/(3)xy在不连续二次多项式扰动下的极限环分支问题.结果表明该系统从原点的周期环域最多可以分支出4个极限环.并且,这个上界是可以达到的.

关键词: 极限环, 不连续微分系统, 平均法, 二次等时系统

Abstract:

In this paper, we bound the number of limit cycles which bifurcate from the period annulus of a class of quadratic isochronous center ?=-y-(4)/(3)x2,?=x-(16)/(3)xy, when perturbed inside the class of all discontinuous quadratic polynomial differential systems. Our results show that there are at most 4 limit cycles bifurcating from this system. Moreover, this bound is sharp.

Key words: Limit cycle, Discontinuous differential system, Averaging method, Quadratic isochronous center

中图分类号: 

  • O175