Sufficient conditions for the existence of periodic solutions of the extended Duffing-Van der Pol oscillator
Euzébio, R (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2016
Abstract:	In this paper, some aspects on the periodic solutions of the extended Duffing-Van der Pol oscillator are discussed. Doing different rescaling of the variables and parameters of the system associated with the extended Duffing-Van der Pol oscillator, we show that it can bifurcate one or three periodic solutions from a two-dimensional manifold filled by periodic solutions of the referred system. For each rescaling we exhibit concrete values for which these bounds are reached. Beyond that we characterize the stability of some periodic solutions. Our approach is analytical and the results are obtained using the averaging theory and some algebraic techniques.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM201340998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 318999 European Commission 316338
Note:	Altres ajuts: ICREA Academia, FEDER-UNAB-104E-378, CAPES grant 88881 and 030454/2013-01 do Programa CSFPVE
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Extended Duffing-Van der Pol oscillator ; Periodic solution ; Non-autonomous systems ; Averaging theory
Published in:	International Journal of Computer Mathematics, Vol. 93, Issue 8 (2016) , p. 1358-1382, ISSN 1029-0265

DOI: 10.1080/00207160.2015.1046847

Postprint 31 p, 691.3 KB

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