Hopf Cyclicity of a Family of Generic Reversible Quadratic Systems with One Center

被引：0
作者：
Ji Hua WANG [1 ]
机构：
[1] School of Mathematics, Sun Yat-sen University
来源：
Acta Mathematica Sinica,English Series | 2019年 / 10期
关键词：
Quadratic reversible system; limit cycle; weak focus; Hopf bifurcation;
D O I：
暂无
中图分类号：
O175 [微分方程、积分方程];
学科分类号：
070104 ;
摘要：
This paper is concerned with small quadratic perturbations to one parameter family of generic reversible quadratic vector fields with a simple center. The first objective is to show that this system exhibits two small amplitude limit cycles emerging from a Hopf bifurcation. The second one we prove that the system has no limit cycle around the weak focus of order two. The results may be viewed as a contribution to proving the conjecture on cyclicity proposed by Iliev(1998).
引用
收藏
页码：1586 / 1594
页数：9
相关论文
共 50 条
  • [31] QUADRATIC PERTURBATIONS OF A CLASS OF QUADRATIC REVERSIBLE SYSTEMS WITH TWO CENTERS
    Coll, Bartomeu
    Li, Chengzhi
    Prohens, Rafel
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 24 (03) : 699 - 729
  • [32] Cyclicity of planar homoclinic loops and quadratic integrable systems
    Han, MA
    SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY, 1997, 40 (12): : 1247 - 1258
  • [33] Cyclicity of planar homoclinic loops and quadratic integrable systems
    Maoan Han
    Science in China Series A: Mathematics, 1997, 40 : 1247 - 1258
  • [34] Cyclicity of planar homoclinic loops and quadratic integrable systems
    韩茂安
    Science China Mathematics, 1997, (12) : 1247 - 1258
  • [35] Center cyclicity of a family of quartic polynomial differential system
    Isaac A. García
    Jaume Llibre
    Susanna Maza
    Nonlinear Differential Equations and Applications NoDEA, 2016, 23
  • [36] Center cyclicity of a family of quartic polynomial differential system
    Garcia, Isaac A.
    Llibre, Jaume
    Maza, Susanna
    NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2016, 23 (03):
  • [37] Center and focus problem and Hopf bifurcation for planar polynomial systems
    Han, Maoan
    LET'S FACE CHAOS THROUGH NONLINEAR DYNAMICS, 2012, 1468 : 176 - 192
  • [38] ON THE NUMBER OF LIMIT CYCLES IN PERTURBATIONS OF A QUADRATIC REVERSIBLE CENTER
    Wu, Juanjuan
    Peng, Linping
    Li, Cuiping
    JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2012, 92 (03) : 409 - 423
  • [39] QUADRATIC PERTURBATIONS OF A CLASS OF QUADRATIC REVERSIBLE LOTKA-VOLTERRA SYSTEMS
    Shao, Yi
    Chunxiang, A.
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2013, 23 (08):
  • [40] The Number of Limit Cycles Bifurcating from a Quadratic Reversible Center
    Liang, Feng
    Liu, Yeqing
    Chen, Chong
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2021, 31 (13):
12345