The same distribution of limit cycles in five perturbed cubic Hamiltonian systems

被引：22

作者：

Liu, ZR ^{[1
]}

Yang, ZY ^{[1
]}

Jiang, T ^{[1
]}

机构：

[1] Yunnan Univ, Dept Math, Inst Appl Math, Kunming 650091, Yunnan, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2003年 / 13卷 / 01期

关键词：

limit cycles; bifurcation; cubic Hamiltonian system;

D O I：

10.1142/S0218127403006522

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using the method of qualitative analysis we show that five perturbed cubic Hamiltonian systems have the same distribution of limit cycles and have 11 limit cycles for some parameters. The accurate location of each limit cycle is given by numerical exploration. In other words, we demonstrate the existence of 11 limit cycles and their distribution in five perturbed systems in two ways, the results obtained from both ways are the same.

引用

页码：243 / 249

页数：7

共 50 条

[21] 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
[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] On the number of limit cycles of a perturbed cubic polynomial differential center
Li, Shimin
Zhao, Yulin
Li, Jun
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 404 (02) : 212 - 220
[24] Fifteen Limit Cycles Bifurcating from a Perturbed Cubic Center
Menaceur, Amor
Alrawashdeh, Mufda
Idris, Sahar Ahmed
Abd-Elmageed, Hala
DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2021, 2021
[25] Limit cycles for rigid cubic systems
Gasull, A
Prohens, R
Torregrosa, J
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 303 (02) : 391 - 404
[26] Thirteen limit cycles for a class of Hamiltonian systems under seven-order perturbed terms
Tigan, Gheorghe
CHAOS SOLITONS & FRACTALS, 2007, 31 (02) : 480 - 488
[27] Limit Cycle Bifurcations from an Order-3 Nilpotent Center of Cubic Hamiltonian Systems Perturbed by Cubic Polynomials
Zhang, Li
Wang, Chenchen
Hu, Zhaoping
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2020, 30 (09):
[28] Existence And Distribution Of Limit Cycles In A Hamiltonian System
Tigan, Gheorghe
APPLIED MATHEMATICS E-NOTES, 2006, 6 : 176 - 185
[29] ON THE NUMBER OF LIMIT CYCLES OF A CUBIC NEAR-HAMILTONIAN SYSTEM
Yang, Junmin
Han, Maoan
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 24 (03) : 827 - 840
[30] DISTRIBUTION OF LIMIT CYCLES OF THE PLANAR CUBIC SYSTEM
李继彬
Science China Mathematics, 1985, (01) : 35 - 46

← 1 2 3 4 5 →