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] On the cyclicity of quasi-homogeneous polynomial systems
    Lian, Hairong
    Liu, Changjian
    Yang, Jiazhong
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 516 (02)
  • [42] ANALYTIC INTEGRABILITY OF A CLASS OF PLANAR POLYNOMIAL DIFFERENTIAL SYSTEMS
    Llibre, Jaume
    Valls, Claudia
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2015, 20 (08): : 2657 - 2661
  • [43] The number of limit cycles of a class of polynomial differential systems
    Yao, Haiyan
    Han, Maoan
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (01) : 341 - 357
  • [44] Solution of the Center Problem for a Class of Polynomial Differential Systems
    Liu, Chang Jian
    Llibre, Jaume
    Ramirez, Rafael
    Ramirez, Valentin
    ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2024, 40 (07) : 1685 - 1696
  • [45] Polynomial solutions for a class of fractional differential equations and systems
    Dahmani, Zoubir
    Abdelaoui, Mohamed Amin
    Houas, Mohamed
    JOURNAL OF INTERDISCIPLINARY MATHEMATICS, 2018, 21 (03) : 669 - 680
  • [46] Limit cycles of a class of planar polynomial differential systems
    Debz, Nassima
    Boulfoul, Amel
    Berkane, Abdelhak
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (17) : 13592 - 13614
  • [47] A class of polynomial differential systems with explicit limit cycles
    Bendjeddou, A.
    Kina, A.
    INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS, 2019, 58 (02): : 44 - 53
  • [48] Global centres in a class of quintic polynomial differential systems
    da Cruz, Leonardo P. C.
    Llibre, Jaume
    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2024,
  • [49] Solution of the Center Problem for a Class of Polynomial Differential Systems
    Chang Jian LIU
    Jaume LLIBRE
    Rafael RAMREZ
    Valentn RAMREZ
    ActaMathematicaSinica,EnglishSeries, 2024, (07) : 1685 - 1696
  • [50] Parallelization of the Lyapunov constants and cyclicity for centers of planar polynomial vector fields
    Liang, Haihua
    Torregrosa, Joan
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (11) : 6494 - 6509
12345