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

Jaume Llibre; Xiang Zhang

doi:https://doi.org/10.1016/j.jmaa.2018.07.024

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

Jaume Llibre, Xiang Zhang

Department of Mathematics

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30 Citations (Scopus)

Abstract

© 2018 Elsevier Inc. 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.

Original language	English
Pages (from-to)	537-549
Journal	Journal of Mathematical Analysis and Applications
Volume	467
DOIs	https://doi.org/10.1016/j.jmaa.2018.07.024
Publication status	Published - 1 Nov 2018

Keywords

Discontinuous piecewise linear differential system
Limit cycle
Non-smooth differential system

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https://ddd.uab.cat/record/199322

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abstract = "{\textcopyright} 2018 Elsevier Inc. 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.",

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N2 - © 2018 Elsevier Inc. 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.

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KW - Discontinuous piecewise linear differential system

KW - Limit cycle

KW - Non-smooth differential system

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

Abstract

Keywords

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