On the Limit Cycles Bifurcating from a Quadratic Reversible Center of Genus One

被引：3

作者：

Peng, Linping ^{[1
]}

Li, You ^{[1
]}

机构：

[1] Beihang Univ, Sch Math & Syst Sci, LIMB, Minist Educ, Beijing 100191, Peoples R China

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2014年 / 11卷 / 02期

关键词：

Quadratic reversible system; genus one; period annulus; bifurcation of limit cycles; Abelian integral; UNBOUNDED HETEROCLINIC LOOPS; HAMILTONIAN-SYSTEMS; PERIOD ANNULI; INTEGRABLE SYSTEM; HOMOCLINIC LOOP; HILBERT PROBLEM; PERTURBATIONS; CYCLICITY; N=2;

D O I：

10.1007/s00009-013-0325-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper is concerned with the bifurcation of limit cycles in perturbations of a quadratic reversible system with a center of genus one. By studying the properties of the auxiliary curve and centroid curve defined by the Abelian integrals, we have proved that under small quadratic perturbations, at most two limit cycles arise from the period annulus surrounding the quadratic reversible center, and the bound is sharp. This partially verifies Conjecture 1 given in Gautier et al. (Discrete Contin Dyn Syst 25:511-535, 2009).

引用

页码：373 / 392

页数：20

共 50 条

[21] BIFURCATION OF LIMIT CYCLES FROM A QUADRATIC REVERSIBLE CENTER WITH THE UNBOUNDED ELLIPTIC SEPARATRIX
Peng, L.
Lei, Y.
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2013, 39 (06): : 1223 - 1248
[22] SECOND-ORDER BIFURCATION OF LIMIT CYCLES FROM A QUADRATIC REVERSIBLE CENTER
Peng, Linping
Huang, Bo
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2017,
[23] Bifurcating limit cycles in quadratic polynomial differential systems
Chan, HSY
Chung, KW
Qi, DW
PHYSICA A, 2000, 288 (1-4): : 417 - 423
[24] Algebraic Limit Cycles Bifurcating from Algebraic Ovals of Quadratic Centers
Llibre, Jaume
Tian, Yun
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2018, 28 (12):
[25] A class of quadratic reversible systems with a center of genus one
Xiong, Yanqin
Zhang, Tonghua
CHAOS SOLITONS & FRACTALS, 2018, 114 : 119 - 129
[26] 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
[27] Limit cycles bifurcating from piecewise quadratic systems separated by a straight line
Peng, Linping
Gao, Yunfei
Feng, Zhaosheng
Nonlinear Analysis, Theory, Methods and Applications, 2020, 196
[28] The maximal number of limit cycles bifurcating from a Hamiltonian triangle in quadratic systems
Xiong, Yanqin
Han, Maoan
Xiao, Dongmei
JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 280 : 139 - 178
[29] Limit cycles bifurcating from piecewise quadratic systems separated by a straight line
Peng, Linping
Gao, Yunfei
Feng, Zhaosheng
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2020, 196
[30] CYCLICITY OF SEVERAL QUADRATIC REVERSIBLE SYSTEMS WITH CENTER OF GENUS ONE
Chen, Long
Ma, Xianzhong
Zhang, Gemeng
Li, Chengzhi
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2011, 1 (04): : 439 - 447

← 1 2 3 4 5 →