Limit Cycles Bifurcating from a Class of Cubic Hamiltonian Systems

被引：0

作者：

Chen, Yuanyuan ^{[2
]}

Yu, Jiang ^{[1
]}

机构：

[1] Shanghai Jiao Tong Univ, CMA Shanghai, Sch Math Sci, Shanghai 200240, Peoples R China

[2] Zhongyuan Univ Technol, Coll Sci, Zhengzhou 450000, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2022年 / 32卷 / 06期

关键词：

Near-Hamiltonian system; Abelian integral; limit cycle; DEGREE-4; PERTURBATIONS;

D O I：

10.1142/S0218127422500882

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the perturbation of a class of cubic Hamiltonian systems is considered. Using Abelian integral, we prove that there exists a neighborhood of the center where the system has at most two limit cycles for arbitrary polynomial perturbation of degree three or four, and at most four limit cycles for arbitrary polynomial perturbation of degree five or six, respectively, which can be reached.

引用

页数：16

共 50 条

[21] SAME DISTRIBUTION OF LIMIT CYCLES TO PERTURBED CUBIC HAMILTONIAN SYSTEMS WITH DIFFERENT PERTURBATIONS
Zhiyan Yang
Annals of Applied Mathematics, 2011, 27 (02) : 241 - 247
[22] Bifurcating limit cycles in quadratic polynomial differential systems
Chan, HSY
Chung, KW
Qi, DW
PHYSICA A, 2000, 288 (1-4): : 417 - 423
[23] LIMIT CYCLES OF A QUADRATIC HAMILTONIAN SYSTEM BY CUBIC PERTURBATIONS
Zhao Yong Han Maoan Yang Junmin Institute of MathShanghai Normal UniversityShanghai
Annals of Differential Equations, 2007, (04) : 593 - 602
[24] Limit cycles for a cubic Hamiltonian system with lower perturbations
Liu, Zheng-Rong
Li, Shao-Yong
PROCEEDINGS OF THE 5TH INTERNATIONAL CONFERENCE ON NONLINEAR MECHANICS, 2007, : 1526 - 1529
[25] The number of limit cycles of cubic Hamiltonian system with perturbation
Wu, Cheng-qiang
Xia, Yonghui
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2006, 7 (05) : 943 - 949
[26] Limit cycles bifurcating from a degenerate center
Llibre, Jaume
Pantazi, Chara
MATHEMATICS AND COMPUTERS IN SIMULATION, 2016, 120 : 1 - 11
[27] Limit cycles bifurcating from discontinuous centres
Braga, Denis de Carvalho
Carvalho, Tiago
Mello, Luis Fernando
IMA JOURNAL OF APPLIED MATHEMATICS, 2017, 82 (04) : 849 - 863
[28] Limit Cycles Bifurcating of Discontinuous and Continuous Piecewise Differential Systems of Isochronous Cubic Centers with Three Zones
Anacleto, Maria Elisa
Vidal, Claudio
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2024, 23 (04)
[29] Stability and bifurcations of limit cycles of the equator in a class of cubic polynomial systems
Liu, YR
Chen, H
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2002, 44 (8-9) : 997 - 1005
[30] Conditions for origin to be a center and the bifurcation of limit cycles in a class of cubic systems
ZHU Jiehua and ZHU SimingDepartment of Mathematics
ChineseScienceBulletin, 1997, (14) : 1157 - 1161

← 1 2 3 4 5 →