Limit cycles of discontinuous piecewise polynomial vector fields

被引：8

作者：

de Carvalho, Tiago ^{[1
]}

Llibre, Jaume ^{[2
]}

Tonon, Durval Jose ^{[3
]}

机构：

[1] UNESP, Fac Ciencias, Dept Matemat, Av Engn Luiz Edmundo Carrijo Coube 14-01, BR-17033360 Bauru, SP, Brazil

[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain

[3] Univ Fed Goias, Inst Math & Stat, Ave Esperanca S-N,Campus Samambaia, BR-74690900 Goiania, Go, Brazil

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2017年 / 449卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

Piecewise smooth vector fields; Limit cycle; Averaging theory; Cyclicity; LINEAR SYSTEMS; BIFURCATION; EXISTENCE; NUMBER;

D O I：

10.1016/j.jmaa.2016.11.048

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center (x) over dot = -y((x(2) + y(2))/2)(m) and (y) over dot = x((x(2) + y(2))/2)(m) with m >= 1, when we perturb it inside a class of discontinuous piecewise polynomial vector fields of degree n with k pieces. The positive integers m, n and k are arbitrary. The main tool used for proving our results is the averaging theory for discontinuous piecewise vector fields. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：572 / 579

页数：8

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