On the number of limit cycles of a class of polynomial differential systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)

Date:	2012
Abstract:	We study the number of limit cycles of the polynomial differential systems of the form x˙ = y − g1(x) − f1(x)y, y˙ = −x − g2(x) − f2(x)y, where g1, f1, g2 and f2 are polynomials of a given degree. Note that when g1(x) = f1(x) = 0 we obtain the generalized polynomial Li'enard differential systems. We provide an accurate upper bound of the maximum number of limit cycles that the above system can have bifurcating from the periodic orbits of the linear center ˙x = y, ˙y = −x using the averaging theory of first and second order.
Grants:	Ministerio de Educación y Ciencia MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	Agraïments: The second author has been partially supported by FCT through CAMGSD.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycles ; Polynomial differential systems
Published in:	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012, p. 1-14, ISSN 1471-2946

DOI: 10.1098/rspa.2011.0741

Postprint 13 p, 605.3 KB

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