BIFURCATION OF LIMIT CYCLES BY PERTURBING PIECEWISE HAMILTONIAN SYSTEMS

被引：83
|
作者：
Liu, Xia [1 ]
Han, Maoan [1 ]
机构：
[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2010年 / 20卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Perturbed piecewise Hamiltonian system; Melnikov function; Poincare map; limit cycle; bifurcation; DIFFERENTIAL-EQUATIONS; HOPF CYCLICITY; PLANAR;
D O I：
10.1142/S021812741002654X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, the general perturbation of piecewise Hamiltonian systems on the plane is considered. When the unperturbed system has a family of periodic orbits, similar to the perturbations of smooth system, an expression of the first order Melnikov function is derived, which can be used to study the number of limit cycles bifurcated from the periodic orbits. As applications, the number of bifurcated limit cycles of several concrete piecewise systems are presented.
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页码：1379 / 1390
页数：12
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