On the Number of Limit Cycles of a Z4-equivariant Quintic Near-Hamiltonian System

被引：5

作者：

Sun, Xian Bo ^{[1
]}

Han, Mao An ^{[2
]}

机构：

[1] Guangxi Univ Finance & Econ, Dept Appl Math, Nanning 530003, Peoples R China

[2] Shanghai Normal Univ, Inst Math, Shanghai 200234, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2015年 / 31卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Limit cycle; near-Hamiltonian system; heteroclinic loop; Z(4)-equivariance; Hopf bifurcation; PLANAR VECTOR FIELD; CUBIC SYSTEM; BIFURCATIONS; DISTRIBUTIONS; EXISTENCE;

D O I：

10.1007/s10114-015-2117-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the number of limit cycles of a near-Hamiltonian system having Z(4)-equivariant quintic perturbations. Using the methods of Hopf and heteroclinic bifurcation theory, we find that the perturbed system can have 28 limit cycles, and its location is also given. The main result can be used to improve the lower bound of the maximal number of limit cycles for some polynomial systems in a previous work, which is the main motivation of the present paper.

引用

页码：1805 / 1824

页数：20

共 50 条

[21] Bifurcation of Limit Cycles in a Near-Hamiltonian System with a Cusp of Order Two and a Saddle
Bakhshalizadeh, Ali
Zangeneh, Hamid R. Z.
Kazemi, Rasool
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2016, 26 (11):
[22] Bifurcations and distribution of limit cycles for near-Hamiltonian polynomial systems
Zang, Hong
Wang, Zheng
Zhang, Tonghua
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 348 (01) : 87 - 100
[23] The number of limit cycles for a class of quintic Hamiltonian systems under quintic perturbations
Chen, GW
Wu, YB
Yang, XN
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2002, 73 : 37 - 53
[24] Limit cycles near a homoclinic loop in two classes of piecewise smooth near-Hamiltonian systems
Ma, Deyue
Yang, Junmin
CHAOS SOLITONS & FRACTALS, 2025, 192
[25] On Double Homoclinic Bifurcation of Limit Cycles in Near-Hamiltonian Systems on the Cylinder
Ke, Ai
Yang, Junmin
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2024, 23 (05)
[26] On the Limit Cycles of a Perturbed Z3-Equivariant Planar Quintic Vector Field
Ma, Yunlei
Wu, Yuhai
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2015, 25 (05):
[27] Coexistence of Algebraic Limit Cycles and Small Limit Cycles of Two Classes of Near-Hamiltonian Systems with a Nilpotent Singular Point
Liu, Huimei
Cai, Meilan
Li, Feng
AXIOMS, 2024, 13 (09)
[28] On the Number of Limit Cycles Bifurcated from a Near-Hamiltonian System with a Double Homoclinic Loop of Cuspidal Type Surrounded by a Heteroclinic Loop
Moghimi, Pegah
Asheghi, Rasoul
Kazemi, Rasool
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2018, 28 (01):
[29] LIMIT CYCLE BIFURCATIONS IN NEAR-HAMILTONIAN SYSTEMS BY PERTURBING A NILPOTENT CENTER
Han, Maoan
Jiang, Jiao
Zhu, Huaiping
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2008, 18 (10): : 3013 - 3027
[30] Limit Cycles Near a Centre and a Heteroclinic Loop in a Near–Hamiltonian Differential System
Lijun Wei
Xiang Zhang
Jinbo Zhu
Journal of Dynamics and Differential Equations, 2024, 36 : 405 - 420

← 1 2 3 4 5 →