Limit cycles bifurcating from the periodic orbits of the weight-homogeneous polynomial centers of weight-degree 3
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Lopes, Bruno D. (Universidade Estadual de Campinas (Brasil). Instituto de Matemática, Estatística e Computação Científica)
De Moraes, Jaime Rezende (Universidad Estatal de Mato Grosso del Sur (Brasil))

Date:	2018
Abstract:	In this paper we obtain two explicit polynomials, whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of polynomial differential centers of order 5, when this family is perturbed inside the class of all polynomial differential systems of order 5, whose average function of first order is not zero. Then the maximum number of limit cycles that bifurcate from these periodic orbits is 6 and it is reached. The family of centers studied completes the study about the limit cycles which can bifurcate from the periodic orbits of all centers of the weight--homogeneous polynomial differential systems of weight--degree 3, when we perturb them inside the class of all polynomial differential systems having the same degree, and whose average function of first order is not zero.
Grants:	European Commission 318999 Ministerio de Economía y Competitividad MTM2016-77278-P Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Averaging method ; Limit cycles ; Polinomial vector field ; Weight-homogeneous differential system
Published in:	Electronic journal of differential equations, Vol. 2018, No. 118 (2018) , p. 1-14, ISSN 1072-6691

14 p, 238.1 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles