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

共 50 条

[21] Twelve limit cycles around a singular point in a planar cubic-degree polynomial system [J].

Yu, Pei ;

Tian, Yun .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2014, 19 (08) :2690-2705

[22] Linear estimate for the number of limit cycles of a perturbed cubic polynomial differential system [J].

Llibre, Jaume ;

Wu, Hao ;

Yu, Jiang .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (01) :419-432

[23] A CUBIC DIFFERENTIAL SYSTEM WITH NINE LIMIT CYCLES [J].

Lloyd, Noel G. ;

Pearson, Jane M. .

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2012, 2 (03) :293-304

[24] On the limit cycles for a class of discontinuous piecewise cubic polynomial differential systems [J].

Huang, Bo .

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2020, (25) :1-24

[25] GLOBAL BIFURCATIONS OF LIMIT CYCLES FOR A CUBIC SYSTEM [J].

孟争 ;

韩茂安 ;

顾圣士 .

AnnalsofDifferentialEquations, 2000, (03) :263-269

[26] Limit Cycles Appearing from the Perturbation of a Cubic Isochronous Center [J].

Yang, Jihua ;

Zhang, Qipeng .

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2025, 24 (03)

[27] Global bifurcation of limit cycles in a family of multiparameter system [J].

Xiang, GH ;

Han, MA .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2004, 14 (09) :3325-3335

[28] NEW STUDY ON THE CENTER PROBLEM AND BIFURCATIONS OF LIMIT CYCLES FOR THE LYAPUNOV SYSTEM (I) [J].

Liu, Yirong ;

Li, Jibin .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2009, 19 (11) :3791-3801

[29] On the Bifurcation of Limit Cycles Due to Polynomial Perturbations of Hamiltonian Centers [J].

Colak, Ilker E. ;

Llibre, Jaume ;

Valls, Claudia .

MEDITERRANEAN JOURNAL OF MATHEMATICS, 2017, 14 (02)

[30] NEW STUDY ON THE CENTER PROBLEM AND BIFURCATIONS OF LIMIT CYCLES FOR THE LYAPUNOV SYSTEM (II) [J].

Liu, Yirong ;

Li, Jibin .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2009, 19 (09) :3087-3099

← 1 2 3 4 5 →