THE CENTER-FOCUS PROBLEM AND BIFURCATION OF LIMIT CYCLES IN A CLASS OF 7TH-DEGREE POLYNOMIAL SYSTEMS

被引：3

作者：

Sang, Bo ^{[1
,2
]}

Wang, Qinlong ^{[2
,3
]}

机构：

[1] Liaocheng Univ, Sch Math Sci, Liaocheng 252059, Peoples R China

[2] Hezhou Univ, Guangxi Educ Dept, Key Lab Symbol Computat & Engn Data Proc, Hezhou 542899, Guangxi, Peoples R China

[3] Hezhou Univ, Sch Sci, Hezhou 542899, Peoples R China

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2016年 / 6卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Limit cycle; center variety; singular point value; time-reversibility; INTEGRABILITY; POINTS;

D O I：

10.11948/2016052

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By computing singular point values, the center conditions are established for a class of 7th-degree planar polynomial systems with 15 parameters. It is proved that such systems can have 13 small-amplitude limit cycles in the neighborhood of the origin. To the best of our knowledge, this is the first example of a 7th-degree system having non-homogeneous nonlinearities with thirteen limit cycles bifurcated from a fine focus.

引用

页码：817 / 826

页数：10

共 50 条

[31] Limit cycles for a class of three-dimensional polynomial differential systems
Llibre, Jaume
Yu, Jiang
JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2007, 13 (04) : 531 - 539
[32] Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems
Llibre, Jaume
Lopes, Bruno D.
De Moraes, Jaime R.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2014, 13 (01) : 129 - 148
[33] Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems
Jaume Llibre
Bruno D. Lopes
Jaime R. De Moraes
Qualitative Theory of Dynamical Systems, 2014, 13 : 129 - 148
[34] Number of Limit Cycles from a Class of Perturbed Piecewise Polynomial Systems
Chen, Xiaoyan
Han, Maoan
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2021, 31 (09):
[35] Integrability, degenerate centers, and limit cycles for a class of polynomial differential systems
Gine, J.
Llibre, J.
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2006, 51 (9-10) : 1453 - 1462
[36] On the limit cycles for a class of discontinuous piecewise cubic polynomial differential systems
Huang, Bo
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2020, (25) : 1 - 24
[37] Limit Cycles for a Class of Three-Dimensional Polynomial Differential Systems
Jaume Llibre
Jiang Yu
Journal of Dynamical and Control Systems, 2007, 13 : 531 - 539
[38] Bifurcation of Limit Cycles and Isochronous Centers on Center Manifolds for a Class of Cubic Kolmogorov Systems in R3
Gu, Jieping
Zegeling, Andre
Huang, Wentao
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2023, 22 (02)
[39] Distribution of Limit Cycles for A Class of Higher-Degree Degenerate Plane Polynomial System
Gao, Jie
PROCEEDINGS OF THE 7TH CONFERENCE ON BIOLOGICAL DYNAMIC SYSTEM AND STABILITY OF DIFFERENTIAL EQUATION, VOLS I AND II, 2010, : 598 - 601
[40] On the limit cycles of the piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center
Llibre, Jaume
Salhi, Tayeb
CHAOS SOLITONS & FRACTALS, 2022, 160

← 1 2 3 4 5 →