On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line

In this paper we study the maximum number \(N\) of limit cycles that can exhibit a planar piecewise linear differential system formed by two pieces separated by a straight line. More precisely, we prove that this maximum number satisfies \(2\leq N \leq 3\) if one of the two linear differential syste...

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Bibliographic Details
Published in:arXiv.org 2014-09
Main Authors: Euzébio, Rodrigo D, Llibre, Jaume
Format: Article
Language:English
Subjects:
Discontinuity
Online Access:Get full text
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Summary:In this paper we study the maximum number \(N\) of limit cycles that can exhibit a planar piecewise linear differential system formed by two pieces separated by a straight line. More precisely, we prove that this maximum number satisfies \(2\leq N \leq 3\) if one of the two linear differential systems has its equilibrium point on the straight line of discontinuity.
ISSN:2331-8422
DOI:10.48550/arxiv.1409.4602