华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (5): 73-83.

• 应用数学与基础数学 • 上一篇    下一篇

一类空间二次系统的异维环分支

王丽英   

  1. 张家口职业技术学院 基础部, 河北 张家口 075000
  • 收稿日期:2010-01-01 修回日期:2010-05-01 出版日期:2010-09-25 发布日期:2010-09-25
  • 通讯作者: 王丽英

Heterodimensional cycle bifurcation of a spatial quadratic system

WANG Li-ying   

  1. Department of Foundation, Zhangjiakou Vocational and Technical College, Zhangjiakou Hebei 075000, China
  • Received:2010-01-01 Revised:2010-05-01 Online:2010-09-25 Published:2010-09-25
  • Contact: WANG Li-ying

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摘要： 首次构造了一个具有最低维数(3维)的二次非线性系统, 证明了其具有轨道双翻转的异维环,
并运用Silnikov坐标和活动标架法分析了该异维环在3次扰动下的分支情况. 本文给出的构造异维环的方法为构造其他类型的具有或不具有轨道翻转的同宿、异宿和异维环提供了很好的借鉴.

关键词: 异维环, 活动坐标, 异宿轨道, 周期轨道, 分支, 异维环, 活动坐标, 异宿轨道, 周期轨道, 分支

Abstract: A concrete nonlinear system with degree two and the least dimension (=3) was firstly given, and it was shown that the system has a heterodimensional cycle with double orbit flips. Then, by using Silnikov coordinates and moving frame, the bifurcation of the cycle was studied under the perturbation of degree three. The method given here provides a useful reference for constructing homoclinic, heteroclinic and heterodimensional cycles with various other kinds of degeneracy.

Key words: moving frame, heteroclinic orbit, periodic orbit, bifurcations, heterodimensional cycle, moving frame, heteroclinic orbit, periodic orbit, bifurcations

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