Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth systems with a cusp

被引：6
|
作者：
Wei, Lijun [1 ]
机构：
[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2017年 / 38卷
关键词：
Melnikov function; Limit cycle; Generalized homoclinic loop; Cusp; Piecewise smooth system; OSCILLATOR;
D O I：
10.1016/j.nonrwa.2017.05.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For a piecewise analytical Hamiltonian system with a cusp on a switch line, which has a family of periodic orbits near a generalized homoclinic loop, we study the maximum number of limit cycles bifurcating from the periodic orbits. For doing so, we first obtain the asymptotic expressions of the Melnikov functions near the loop. Finally we present two examples illustrating applications of the main results. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码：306 / 326
页数：21
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