Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center

被引：45

作者：

Llibre, Jaume ^{[1
]}

Zhang, Xiang ^{[2
]}

机构：

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

[2] Shanghai Jiao Tong Univ, Minist Educ, Key Lab Sci & Engn Comp, Sch Math Sci, Shanghai 200240, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 467卷 / 01期

关键词：

Non-smooth differential system; Limit cycle; Discontinuous piecewise linear differential system; BIFURCATIONS; NUMBER;

D O I：

10.1016/j.jmaa.2018.07.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

From the beginning of this century more than thirty papers have been published studying the limit cycles of the discontinuous piecewise linear differential systems with two pieces separated by a straight line, but it remains open the following question: what is the maximum number of limit cycles that this class of differential systems can have? Here we prove that when one of the linear differential systems has a center, real or virtual, then the discontinuous piecewise linear differential system has at most two limit cycles. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：537 / 549

页数：13

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