Limit cycles of discontinuous piecewise linear differential systems
Cardin, Pedro Toniol (Universidade Estadual Paulista (Brasil))
de Carvalho, Tiago (Universidade Estadual Paulista (Brasil))
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2011
Abstract:	We study the bifurcation of limit cycles from the periodic orbits of a two-dimensional (resp. four-dimensional) linear center in Rn perturbed inside a class of discontinuous piecewise linear differential systems. Our main result shows that at most 1 (resp. 3) limit cycle can bifurcate up to first-order expansion of the displacement function with respect to the small parameter. This upper bound is reached. For proving these results, we use the averaging theory in a form where the differentiability of the system is not needed.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	Agraïments: The two first authors are partially supported by a FAPESP-BRAZIL grant 2007/07957-8 and grant 2007/08707-5 r espectively.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Discontinuous piecewise linear differential systems ; Limit cycles ; Averaging theory
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 21 Núm. 11 (2011) , p. 3181-3194, ISSN 1793-6551

DOI: 10.1142/S0218127411030441

Postprint 22 p, 400.9 KB

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