The centers and their cyclicity for a class of polynomial differential systems of degree 7

被引：3
|
作者：
Benterki, Rebiha [1 ]
Llibre, Jaume [2 ]
机构：
[1] Univ Bachir El Ibrahimi, Dept Math, Bordj Bou Arreridj 34265, El Anasser, Algeria
[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2020年 / 368卷 / 368期
基金：
欧盟地平线“2020”;
关键词：
Center; Phase portrait; Cyclicity; Limit cycle; Hopf bifurcation; Averaging method;
D O I：
10.1016/j.cam.2019.112456
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We classify the global phase portraits in the Poincare disc of the generalized Kukles systems (x) over dot = -y, (y) over dot = x + axy(6 )+ bx(3)y(4 )+ cx(5)y(2 )+ dx(7), which are symmetric with respect to both axes of coordinates. Moreover using the averaging theory up to sixth order, we study the cyclicity of the center located at the origin of coordinates, i.e. how many limit cycles can bifurcate from the origin of coordinates of the previous differential system when we perturb it inside the class of all polynomial differential systems of degree 7. (C) 2019 Elsevier B.V.All rights reserved.
引用
收藏
页数：16
相关论文
共 50 条
  • [41] Limit Cycles for a Class of Three-Dimensional Polynomial Differential Systems
    Jaume Llibre
    Jiang Yu
    Journal of Dynamical and Control Systems, 2007, 13 : 531 - 539
  • [42] Limit Cycles of a Class of Polynomial Differential Systems Bifurcating from the Periodic Orbits of a Linear Center
    Menaceur, Amor
    Boulaaras, Salah
    Alkhalaf, Salem
    Jain, Shilpi
    SYMMETRY-BASEL, 2020, 12 (08): : 1 - 15
  • [43] Z2-SYMMETRIC PLANAR POLYNOMIAL HAMILTONIAN SYSTEMS OF DEGREE 3 WITH NILPOTENT CENTERS
    Dias, Fabio Scalco
    Llibre, Jaume
    Valls, Claudia
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2019,
  • [44] Limit cycles by perturbing quadratic isochronous centers inside piecewise polynomial differential systems
    Cen, Xiuli
    Liu, Changjian
    Yang, Lijun
    Zhang, Meirong
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 265 (12) : 6083 - 6126
  • [45] Limit cycles of cubic polynomial differential systems with rational first integrals of degree 2
    Llibre, Jaume
    Lopes, Bruno D.
    de Moraes, Jaime R.
    APPLIED MATHEMATICS AND COMPUTATION, 2015, 250 : 887 - 907
  • [46] The cyclicity of a class of quadratic reversible systems with hyperelliptic curves
    Sun, Yangjian
    Ji, Guilin
    Wang, Shaoqing
    BULLETIN DES SCIENCES MATHEMATIQUES, 2024, 193
  • [47] CYCLICITY OF UNBOUNDED SEMI-HYPERBOLIC 2-SADDLE CYCLES IN POLYNOMIAL LIENARD SYSTEMS
    Caubergh, Magdalena
    Dumortier, Freddy
    Luca, Stijn
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 27 (03) : 963 - 980
  • [48] Centers and isochronous centers of a class of quasi-analytic switching systems
    Feng Li
    Pei Yu
    Yirong Liu
    Yuanyuan Liu
    Science China Mathematics, 2018, 61 : 1201 - 1218
  • [49] Centers and isochronous centers of a class of quasi-analytic switching systems
    Feng Li
    Pei Yu
    Yirong Liu
    Yuanyuan Liu
    ScienceChina(Mathematics), 2018, 61 (07) : 1201 - 1218
  • [50] The Limit Cycle for A Class of Higher Degree Polynomial System
    Wang, Xiaoxia
    Wang, Chengwen
    PROCEEDINGS OF THE 7TH CONFERENCE ON BIOLOGICAL DYNAMIC SYSTEM AND STABILITY OF DIFFERENTIAL EQUATION, VOLS I AND II, 2010, : 717 - 721
12345