Bifurcation of limit cycles by perturbing a class of hyper-elliptic Hamiltonian systems of degree five

被引：17

作者：

Xiong, Yanqin ^{[1
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 411卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Bifurcation; Lienard system; Hamiltonian system; LIENARD SYSTEMS; LOOP;

D O I：

10.1016/j.jmaa.2013.06.073

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate a class of hyper-elliptic Hamiltonian systems of degree five under the polynomial perturbation of degree m + 1. First, we study the number of different phase portraits of the unperturbed system when it has a class of family of periodic orbits and prove that the number is 40. Then, we consider the limit cycle bifurcations and obtain some new results on the lower bound of the maximal number of limit cycles for these systems. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：559 / 573

页数：15

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