Bifurcations of limit cycles in a Z6-equivariant planar vector field of degree 7

被引：1

作者：

Shi, Jian-ping ^{[1
]}

Li, Ji-bin ^{[1
]}

机构：

[1] Kunming Univ Sci & Technol, Ctr Nonlinear Sci Studies, Kunming 650093, Yunnan, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 244卷

关键词：

Bifurcations of limit cycles; Z(6)-equivariant planar vector field; Detection function; Heteroclinic and homoclinic loops; Perturbed Hamiltonian system; HAMILTONIAN SYSTEM; NUMBER;

D O I：

10.1016/j.amc.2014.06.091

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the weakened Hilbert's 16th problem for symmetric planar perturbed polynomial Hamiltonian systems is considered. With the help of numerical analysis, by using bifurcation theory of planar dynamical systems and the method of detection function, we show that a Z(6)-equivariant planar perturbed Hamiltonian vector field of degree 7 has at least 37 limit cycles. The paper also shows the configuration of compound eyes of that Z(6)-equivariant system. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：191 / 200

页数：10

共 50 条

[21] Bifurcation of limit cycles in cubic integrable Z2-equivariant planar vector fields
Yu P.
Han M.
Li J.
Qualitative Theory of Dynamical Systems, 2010, 9 (1-2) : 221 - 233
[22] Limit cycles of a planar vector field
Makhaniok, M
Hesser, J
Noehte, S
Manner, R
ACTA APPLICANDAE MATHEMATICAE, 1997, 48 (01) : 13 - 32
[23] Limit Cycles of a Planar Vector Field
M. Makhaniok
J. Hesser
S. Noehte
R. Männer
Acta Applicandae Mathematica, 1997, 48 : 13 - 32
[24] BIFURCATIONS OF LIMIT CYCLES IN A CLASS OF QUARTIC PLANAR VECTOR FIELDS
Chang, Yuan
Zhao, Liqin
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2025, 15 (04): : 2356 - 2380
[25] Bifurcation of small limit cycles in Z5-equivariant planar vector fields of order 5
Yao, W. H.
Yu, P.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 328 (01) : 400 - 413
[26] Equivalence on bifurcations of multiple limit cycles of planar vector fields of degree 5 with different perturbation terms
Li, Jing
Tian, Yun
Zhang, Wei
Miao, Sufen
DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES B-APPLICATIONS & ALGORITHMS, 2007, 14 : 21 - 23
[27] AN IMPROVED LOWER BOUND ON THE NUMBER OF LIMIT CYCLES BIFURCATING FROM A HAMILTONIAN PLANAR VECTOR FIELD OF DEGREE 7
Johnson, Tomas
Tucker, Warwick
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2010, 20 (05): : 1451 - 1458
[28] On the limit cycles of a quintic planar vector field
Yu-hai Wu
Li-xin Tian
Mao-an Han
Science in China Series A: Mathematics, 2007, 50 : 925 - 940
[29] On the limit cycles of a quintic planar vector field
Wu, Yu-hai
Tian, Li-xin
Han, Mao-an
SCIENCE IN CHINA SERIES A-MATHEMATICS, 2007, 50 (07): : 925 - 940
[30] On the limit cycles of a quintic planar vector field
Yu-hai WU~(1+) Li-xin TIAN~1 Mao-an HAN~2 1 Department of Mathematics
2 Department of Mathematics
ScienceinChina(SeriesA:Mathematics), 2007, (07) : 925 - 940

← 1 2 3 4 5 →