Lower bounds for the maximum number of limit cycles of discontinuous piecewise linear differential systems witha a straight line of separation
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Teixeira, Marco Antonio (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)

Additional title:	On the maximum number of limit cycles of discontinuous piecewise linear differential systems with a straight line of separation
Date:	2013
Abstract:	In this paper we study the maximum number of limit cycles for planar discontinuous piecewise linear differential systems defined in two half-planes separated by a straight line. Here we only consider non-sliding limit cycles. For that systems, the interior of any limit cycle only contains a unique singular point or a unique sliding segment. Moreover, the linear differential systems that we consider in every half-plane can have either a focus (F), or a node (N), or a saddle (S), these equilibrium points can be real or virtual. Then, we can consider six kinds of planar discontinuous piecewise linear differential systems: FF, FN, FS, NN, NS, SS. We analyze for each of these types of discontinuous differential systems the maximum number of known limit cycles.
Grants:	Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	El títol de la versió pre-print de l'article és: On the maximum number of limit cycles of discontinuous piecewise linear differential systems with a straight line of separation
Note:	Agraïments: The second author is partially supported by the FAPESP-BRAZIL grant 2007/06896-5. All the authors are also supported by the joint project CAPES-MECD grant PHB-2009-0025-PC.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Non-smooth differential system ; Limit cycle ; Piecewise linear differential system
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 23 Núm. 4 (2013) , p. 1350066 (10 pages), ISSN 1793-6551

DOI: 10.1142/S0218127413500661

Postprint 14 p, 377.1 KB

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