LIMIT CYCLE BIFURCATIONS NEAR GENERALIZED HOMOCLINIC LOOP IN PIECEWISE SMOOTH DIFFERENTIAL SYSTEMS

被引：14

作者：

Wei, Lijun ^{[1
]}

Zhang, Xiang ^{[2
]}

机构：

[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[2] Shanghai Jiao Tong Univ, Dept Math, MOE LSC, Shanghai 200240, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2016年 / 36卷 / 05期

关键词：

Piecewise smooth system; generalized homoclinic loop; Melnikov function; limit cycle bifurcation; nilpotent saddle; HAMILTONIAN SYSTEM; CUSPIDAL LOOP; PERTURBATIONS; EXISTENCE; UNIQUENESS; EQUATIONS;

D O I：

10.3934/dcds.2016.36.2803

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the maximum number of limit cycles, which can be bifurcated from periodic orbits of planar piecewise smooth Hamiltonian systems, which are located in a neighborhood of a generalized homoclinic loop with a nilpotent saddle on a switch line. First we present asymptotic expressions of the Melnikov functions near the loop. Then using these expressions we study the number of limit cycles which are bifurcated from the periodic orbits near the homoclinic loop under small perturbations. Finally we provide two concrete examples showing applications of our main results.

引用

页码：2803 / 2825

页数：23

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