On the limit cycles of planar discontinuous piecewise linear differential systems with a unique equilibrium
Li, Shimin (Guangdong University of Finance and Economics. School of Mathematics and Statistics (China))
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2019
Abstract:	This paper deals with planar discontinuous piecewise linear differential systems with two zones separated by a vertical straight line x = k. We assume that the left linear differential system (x < k) and the right linear differential system (x > k) share the same equilibrium, which is located at the origin O(0, 0) without loss of generality. Our results show that if k = 0, that is when the unique equilibrium O(0, 0) is located on the line of discontinuity, then the discontinuous piecewise linear differential systems have no crossing limit cycles. While for the case k ≠ 0 we provide lower and upper bounds for the number of limit cycles of these planar discontinuous piecewise linear differential systems depending on the type of their linear differential systems, i. e. if those systems have foci, centers, saddles or nodes, see Table 2.
Grants:	Ministerio de Economía y Competitividad MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycle ; Piecewise discontinuous linear systems
Published in:	Discrete and continuous dynamical systems. Series B, Vol. 24, Issue 11 (November 2019) , p. 5885-5901, ISSN 1553-524X

DOI: 10.3934/dcdsb.2019111

Postprint 18 p, 773.2 KB

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