Center problem and the bifurcation of limit cycles for a cubic polynomial system

被引：10

作者：

Du, Chaoxiong ^{[1
]}

Huang, Wentao ^{[2
]}

Zhang, Qi ^{[3
]}

机构：

[1] Hunan Shaoyang Univ, Dept Math, Shaoyang 422000, Hunan, Peoples R China

[2] Hezhou Univ, Dept Math, Hezhou 542800, Guangxi, Peoples R China

[3] Cent South Univ, Sch Math, Changsha 410075, Hunan, Peoples R China

来源：

APPLIED MATHEMATICAL MODELLING | 2015年 / 39卷 / 17期

基金：

中国国家自然科学基金;

关键词：

Focal value; Bifurcation; Limit cycle; Simultaneous center; FOCUS;

D O I：

10.1016/j.apm.2015.03.037

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this study, we consider the center problem and the bifurcation of limit cycles for a cubic system that lies in a symmetrical vector field about the origin. By analyzing and calculating the focal values (or the Lyapunov constant), we obtain the conditions where two equilibrium points, (1,1) and (-1, -1), become a pair of simultaneous centers. Moreover, six limit cycles, including three stable limit cycles, can bifurcate from (1,1) under a specific condition. From the symmetric quality, (-1, -1) can also bifurcate into six limit cycles by simultaneous Hopf bifurcation, which is an interesting result. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：5200 / 5215

页数：16

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