Limit cycles of generalized Liénard polynomial differential systems via averaging theory
García, Belen (Universidad de Oviedo. Departamento de Matemáticas)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Suárez Pérez del Río, Jesús (Universidad de Oviedo. Departamento de Matemáticas)

Date:	2014
Abstract:	Using the averaging theory of first and second order we study the maximum number of limit cycles of the polynomial differential systems x˙ = y, y˙ = −x − ε(p1(x)y + q1(x)y2) − ε2(p2(x)y + q2(x)y2). which bifurcate from the periodic orbits of the linear center ˙x = y, ˙y = −x. Here ε is a small parameter. If the degrees of the polynomials p1, p2, q1 and q2 is n, then we prove that this maximum number is [n/2] using the averaging theory of first order, where [·] denotes the integer part function; and this maximum number is at most n using the averaging theory of second order.
Grants:	Ministerio de Economía y Competitividad MTM2011-22956 Ministerio de Ciencia e Innovación MTM 2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 316338 European Commission 318999
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Averaging theory ; Liénard Equations ; Limit cycles
Published in:	Chaos, solitons and fractals, Vol. 62-63 (2014) , p. 1-9, ISSN 0960-0779

DOI: 10.1016/j.chaos.2014.02.008

Postprint 16 p, 714.6 KB

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