Limit cycle bifurcations near a generalized homoclinic loop in piecewise smooth systems with a hyperbolic saddle on a switch line

被引：8
|
作者：
Wei, Lijun [1 ]
Liang, Feng [1 ]
Lu, Shiping [1 ,2 ]
机构：
[1] Anhui Normal Univ, Coll Math & Comp Sci, Wuhu 241000, Anhui, Peoples R China
[2] NUIST, Coll Math & Stat, Nanjing 210044, Jiangsu, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 243卷
关键词：
Melnikov function; Limit cycle bifurcation; Generalized homoclinic loop; Piecewise smooth system; Near-Hamiltonian system;
D O I：
10.1016/j.amc.2014.05.041
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we suppose a planar piecewise Hamiltonian system has a generalized homoclinic loop with a hyperbolic saddle on a switch line, and assume that there are two families of periodic orbits on both sides of the loop. Under perturbations we first give the expansion of the first Melnikov function near the loop. Then by using the first coefficients in the expansion, we study the number of limit cycles bifurcating from the homoclinic loop. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：298 / 310
页数：13
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