Limit cycles bifurcating from the periodic orbits of a discontinuous piecewise linear differential center with two zones
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Novaes, Douglas D. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Teixeira, Marco Antonio (Universidade Estadual de Campinas (Brazil). Departamento de Matemática)

Date:	2015
Abstract:	We study a class of discontinuous piecewise linear differential systems with two zones separated by the straight line x = 0. In x > 0 we have a linear saddle with its equilibrium point living in x > 0, and in x < 0 we have a linear differential center. Let p be the equilibrium point of this linear center, when p lives in x < 0, we say that its is real, and when p lives in x > 0 we say that it is virtual. We assume that this discontinuous piecewise linear differential systems formed by the center and the saddle has a center q surrounded by periodic orbits ending in a homoclinic orbit of the saddle, independent if p is real, virtual or p is in x = 0. Note that q = p if p is real or p is in x = 0. We perturb these three classes of systems, according to the position of p, inside the class of all discontinuous piecewise linear differential systems with two zones separated by x = 0. Let N be the maximum number of limit cycles which can bifurcate from the periodic solutions of the center q with these perturbations. Our main results show that N = 2 when p is on x = 0, and N ≥ 2 when p is a real or virtual center.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999
Note:	Agraïments: FEDER-UNAB 10-4E-378. The second author is partially supported by a FAPESP-BRAZIL grant 2013/16492-0. The third authors is partially supported by a FAPESP-BRAZIL grant 2012/18780-0. The three authors are also supported by a CAPES CSF-PVE grant 88881.030454/ 2013-01 from the program CSF-PVE.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Discontinuous differential system ; Limit cycles ; Piecewise linear differential system
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 25 Núm. 11 (2015) , p. 1550144 (11 pages), ISSN 1793-6551

DOI: 10.1142/S0218127415501448

Postprint 15 p, 389.8 KB

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