Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center
type: Item
instance of: scholarly article
title: Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center
zbMATH Open document ID: 1411.34030
author: Jaume Llibre
author: Xiang Zhang
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-08-15T00:00:00Z
full work available at URL: http://ddd.uab.cat/record/199322
review text: The objective of this paper is the upper bound for the maximum number of limit cycles that a planar discontinuous piecewise linear differential systems with two pieces separated by a straight line can have, when there is no a singularity of the two linear differential systems on the discontinuity straight line. The main result is formulated as follows: if one of the two linear differential systems has a center, real or virtual, then the discontinuous piecewise linear differential system has at most two limit cycles. More precisely, two limit cycles can appear only in the case that the focus is real. To prove it the authors use the canonical forms of all the possible configurations of the discontinuous piecewise linear differential systems in \(\mathbb{R}^2\) with two pieces separated by a straight line when both systems have a singularity.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 6918465
zbMATH Keywords: non-smooth differential system
zbMATH Keywords: limit cycle
zbMATH Keywords: discontinuous piecewise linear differential system
MaRDI profile type: Publication
OpenAlex ID: W2884876477
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DOI: 10.1016/J.JMAA.2018.07.024
description: scientific article; zbMATH DE number 6918465