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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.
Note: Número d'acord de subvenció MINECO/MTM2016-77278-P
Note: Número d'acord de subvenció AGAUR/2017/SGR-1617
Note: Número d'acord de subvenció EC/H2020/777911
Rights: Tots els drets reservats.
Language: Anglès
Document: article ; recerca ; acceptedVersion
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 1531-3492

DOI: 10.3934/dcdsb.2019111


Postprint
18 p, 773.2 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2020-04-15, last modified 2020-12-03



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