数学物理学报 ›› 2015, Vol. 35 ›› Issue (1): 83-96.

• 论文 • 上一篇    下一篇

一类非光滑对称三次系统的全局分支

 尚德生, 张耀明   

  1. 山东理工大学理学院, 淄博 255049 
  • 收稿日期:2013-06-08 修回日期:2014-05-06 出版日期:2015-02-25 发布日期:2015-02-25
  • 基金资助:

    山东省自然科学基金重点项目(Zr2010AZ003)资助

Global Bifurcation of A Symmetric Cubic System

 SHANG De-Sheng, ZHANG Yao-Ming   

  1. School of Science, Shandong University of Technology,
    Shandong Zibo 255049
  • Received:2013-06-08 Revised:2014-05-06 Online:2015-02-25 Published:2015-02-25

摘要:

该文对一类对称三次 Hamilton 系统在非光滑对称摄动下产生的极限环数目进行研究.通过多参数摄动理论和定性分析方法,
得到这类在非光滑摄动下的三次系统可以存在至少$\!19$个极限环.

关键词: 摄动, 非光滑三次系统, 同宿轨, 极限环

Abstract:

The number of limit cycles of a  class of symmetric cubic near-Hamiltonian system under symmetric non-smooth perturbations are investigated in this paper.  At least 19 limit cycles are found in this class of perturbed non-smooth cubic system by using the method of  multi-parameter perturbation theory and qualitative analysis.

Key words: Perturbation, Non-smooth cubic system, Homoclinic loop, Limit cycle

中图分类号: 

  • 34C05