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.
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页数：16
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