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Página principal > Artículos > Artículos publicados > Limit cycles of generalized Liénard polynomial differential systems via averaging theory |
Fecha: | 2014 |
Resumen: | 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. |
Ayudas: | 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 |
Derechos: | Tots els drets reservats. |
Lengua: | Anglès |
Documento: | Article ; recerca ; Versió acceptada per publicar |
Materia: | Averaging theory ; Liénard Equations ; Limit cycles |
Publicado en: | Chaos, solitons and fractals, Vol. 62-63 (2014) , p. 1-9, ISSN 0960-0779 |
Postprint 16 p, 714.6 KB |