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

页数：16

共 50 条

[21] Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems
Llibre, Jaume
Lopes, Bruno D.
De Moraes, Jaime R.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2014, 13 (01) : 129 - 148
[22] Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems
Jaume Llibre
Bruno D. Lopes
Jaime R. De Moraes
Qualitative Theory of Dynamical Systems, 2014, 13 : 129 - 148
[23] The maximum number of centers for planar polynomial Kolmogorov differential systems
He, Hongjin
Xiao, Dongmei
JOURNAL OF DIFFERENTIAL EQUATIONS, 2024, 395 : 106 - 124
[24] On general algebraic mechanisms for producing centers in polynomial differential systems
Christopher, Colin
Schlomiuk, Dana
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2008, 3 (02) : 331 - 351
[25] On the cyclicity of quasi-homogeneous polynomial systems
Lian, Hairong
Liu, Changjian
Yang, Jiazhong
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 516 (02)
[26] On general algebraic mechanisms for producing centers in polynomial differential systems
Colin Christopher
Dana Schlomiuk
Journal of Fixed Point Theory and Applications, 2008, 3 : 331 - 351
[27] LIMIT CYCLES FOR TWO CLASSES OF PLANAR POLYNOMIAL DIFFERENTIAL SYSTEMS WITH UNIFORM ISOCHRONOUS CENTERS
Huang, Bo
Niu, Wei
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2019, 9 (03): : 943 - 961
[28] Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four
Saez, Eduardo
Stange, Eduardo
Szanto, Ivan
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2007, 57 (01) : 105 - 114
[29] Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four
Eduardo Sáez
Eduardo Stange
Iván Szántó
Czechoslovak Mathematical Journal, 2007, 57 : 105 - 114
[30] THE CENTER-FOCUS PROBLEM AND BIFURCATION OF LIMIT CYCLES IN A CLASS OF 7TH-DEGREE POLYNOMIAL SYSTEMS
Sang, Bo
Wang, Qinlong
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2016, 6 (03): : 817 - 826

← 1 2 3 4 5 →