Homoclinic Bifurcations in Planar Piecewise-Linear Systems

被引：4
|
作者：
Xu, Bin [1 ]
Yang, Fenghong [2 ]
Tang, Yun [1 ]
Lin, Mu [2 ]
机构：
[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
[2] Cent Univ Finance & Econ, Sch Appl Math, Beijing 100084, Peoples R China
来源：
DISCRETE DYNAMICS IN NATURE AND SOCIETY | 2013年 / 2013卷
关键词：
D O I：
10.1155/2013/732321
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The problem of homoclinic bifurcations in planar continuous piecewise-linear systems with two zones is studied. This is accomplished by investigating the existence of homoclinic orbits in the systems. The systems with homoclinic orbits can be divided into two cases: the visible saddle-focus (or saddle-center) case and the case of twofold nodes with opposite stability. Necessary and sufficient conditions for the existence of homoclinic orbits are provided for further study of homoclinic bifurcations. Two kinds of homoclinic bifurcations are discussed: one is generically related to nondegenerate homoclinic orbits; the other is the discontinuity induced homoclinic bifurcations related to the boundary. The results show that at least two parameters are needed to unfold all possible homoclinc bifurcations in the systems.
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页数：9
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