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

Date:	2013
Abstract:	We study the number of limit cycles of the polynomial differential systems of the form x˙ = y − g1(x), y˙ = −x − g2(x) − f(x)y, where g1(x) = εg11(x)+ε2g12(x)+ε3g13(x), g2(x) =εg21(x) + ε2g22(x) + ε3g23(x) and f(x) = εf1(x) + ε2f2(x) + ε3f3(x) where g1i, g2i, f2i have degree k, m and n respectively for each i = 1, 2, 3, and ε is a small parameter. Note that when g1(x) = 0 we obtain the generalized Li'enard polynomial differential systems. We provide an upper bound of the maximum number of limit cycles that the previous differential system can have bifurcating from the periodic orbits of the linear center ˙x = y, ˙y = −x using the averaging theory of third order.
Grants:	Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	Agraïments: The second author has been supported by the grant AGAUR PIV-DGR-2010 and by FCT through CAMGSD.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 23 Núm. 3 (2013) , p. 1350048 (16 pages), ISSN 1793-6551

DOI: 10.1142/S021812741350048X

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