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
收藏
页码：5200 / 5215
页数：16
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