Bifurcation of limit cycle from a n-dimensional linear center inside a class of piecewise linear differential systems
Cardin, Pedro Toniol (IBILCE-UNESP(Brazil))
de Carvalho, Tiago (IBILCE-UNESP(Brazil))
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2012
Abstract:	Let n be an even integer. We study the bifurcation of limit cycles from the periodic orbits of the n-dimensional linear center given by the differential system x˙ 1 = −x2, x˙ 2 = x1, . . . , x˙ n−1 = −xn, x˙ n = xn−1, perturbed inside a class of piecewise linear differential systems. Our main result shows that at most (4n − 6)n/2−1 limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small parameter. For proving this result we use the averaging theory in a form where the differentiability of the system is not needed.
Grants:	Ministerio de Ciencia e Innovación 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 respec- tively.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycles ; Bifurcation ; Control systems ; Averaging method ; Piecewise linear differential systems ; Center
Published in:	Nonlinear Analysis : Theory, Methods and Applications, Vol. 75 (2012) , p. 143-152, ISSN 0362-546X

DOI: 10.1016/j.na.2011.08.013

Postprint 15 p, 798.6 KB

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