On the Number of Limit Cycles of a Z4-equivariant Quintic Near-Hamiltonian System

被引：5

作者：

Sun, Xian Bo ^{[1
]}

Han, Mao An ^{[2
]}

机构：

[1] Guangxi Univ Finance & Econ, Dept Appl Math, Nanning 530003, Peoples R China

[2] Shanghai Normal Univ, Inst Math, Shanghai 200234, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2015年 / 31卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Limit cycle; near-Hamiltonian system; heteroclinic loop; Z(4)-equivariance; Hopf bifurcation; PLANAR VECTOR FIELD; CUBIC SYSTEM; BIFURCATIONS; DISTRIBUTIONS; EXISTENCE;

D O I：

10.1007/s10114-015-2117-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the number of limit cycles of a near-Hamiltonian system having Z(4)-equivariant quintic perturbations. Using the methods of Hopf and heteroclinic bifurcation theory, we find that the perturbed system can have 28 limit cycles, and its location is also given. The main result can be used to improve the lower bound of the maximal number of limit cycles for some polynomial systems in a previous work, which is the main motivation of the present paper.

引用

页码：1805 / 1824

页数：20

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