Homoclinic bifurcation with nonhyperbolic equilibria

被引：8
|
作者：
Liu, Xingbo [1 ]
Fu, Xianlong [1 ]
Zhu, Deming [1 ]
机构：
[1] E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2007年 / 66卷 / 12期
基金：
中国国家自然科学基金;
关键词：
pitchfork bifurcation; homoclinic orbit; periodic orbit; local coordinate system;
D O I：
10.1016/j.na.2006.04.014
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The problem of homoclinic bifurcation is studied for a high dimensional system with nonhyperbolic equilibria. By constructing local coordinate systems near the unperturbed homoclinic orbit, Poincare maps for the new system are established. Then the persistence of the homoclinic orbit and the bifurcation of the periodic orbit for the system accompanied with pitchfork bifurcation are obtained. Some known results are extended. (c) 2006 Elsevier Ltd. All rights reserved.
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页码：2931 / 2939
页数：9
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