DEGENERATE BIFURCATIONS OF HETERODIMENSIONAL CYCLES WITH ORBIT FLIP

被引：3
|
作者：
Liu, Xingbo [1 ]
Liu, Junying [1 ]
Zhu, Deming [1 ]
机构：
[1] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2013年 / 23卷 / 05期
关键词：
Bifurcation; heterodimensional cycle; orbit flip; local coordinates; HOMOCLINIC ORBITS; UNFOLDINGS;
D O I：
10.1142/S0218127413500806
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, nongeneric bifurcation analysis near heterodimensional cycles with orbit flip is investigated for three-dimensional systems. With the aid of a suitable local coordinate system, the Poincare map is constructed. By means of the bifurcation equations, the existence, nonexistence, coexistence and uniqueness of homoclinic orbit, periodic orbits and the heterodimensional cycle are studied, the relevant bifurcation surfaces and their existing regions are given. Some known results are extended. An example is given to show the existence of the system which has a heterodimensional cycle with orbit flip.
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收藏
页数：18
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