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
相关论文
共 16 条
[1]   General center conditions and bifurcation of limit cycles for a quasi-symmetric seventh degree system [J].
Do, Chaoxiong ;
Liu, Yirong .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (11) :2957-2969
[2]   Limit Cycles Bifurcations for a Class of Kolmogorov Model in Symmetrical Vector Field [J].
Du Chaoxiong ;
Liu Yirong ;
Huang Wentao .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2014, 24 (03)
[3]   Three-Dimensional Hopf Bifurcation for a Class of Cubic Kolmogorov Model [J].
Du Chaoxiong ;
Wang Qinlong ;
Huang Wentao .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2014, 24 (03)
[4]   Center-focus problem and limit cycles bifurcations for a class of cubic Kolmogorov model [J].
Du, Chaoxiong ;
Huang, Wentao .
NONLINEAR DYNAMICS, 2013, 72 (1-2) :197-206
[5]   The bifurcation of limit cycles in Zn-equivariant vector fields [J].
Du, Chaoxiong ;
Liu, Yirong ;
Chen, Haibo .
APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (05) :2041-2056
[6]   The problem of general center-focus and bifurcation of limit cycles for a planar system of nine degrees [J].
Du, Chaoxiong ;
Liu, Yirong .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 223 (02) :1043-1057
[7]  
Kuno E., 1987, ADV ECOL RES, V16, P252
[8]  
Li J., 2010, Qual. Theory Dyn. Syst, V9, P167, DOI [10.1007/s12346-010-0024-7, DOI 10.1007/S12346-010-0024-7, DOI 10.1007/S12346-010-0024-7)]
[9]   Hilbert's 16th problem and bifurcations of planar polynomial vector fields [J].
Li, JB .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2003, 13 (01) :47-106
[10]  
Liu Y., 2008, Singular Point Values, Center Problem and Bifurcations of Limit Cycles of Two Dimensional Differential Autonomous Systems
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