Hopf and homoclinic bifurcations for near-Hamiltonian systems

被引：44

作者：

Tian, Yun ^{[1
]}

Han, Maoan ^{[1
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 262卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Homoclinic loop; Hamiltonian system; Melnikov function; Limit cycle; COMPLETE ABELIAN-INTEGRALS; LIMIT-CYCLES; EXPONENTIAL ESTIMATE; NUMBER; ZEROS; CYCLICITY;

D O I：

10.1016/j.jde.2016.11.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study homoclinic bifurcation of limit cycles in perturbed planar Hamiltonian systems. Suppose that a homoclinic loop is defined by H = h(s). Our main result is that anew method is established for computing the coefficients of the expansion of Melnikov functions at h = h(s). Then by using those coefficients, more limit cycles would be found around homoclinic loops. An example is also provided to illustrate our method. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：3214 / 3234

页数：21

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