Algebraic limit cycles bifurcating from algebraic ovals of quadratic centers
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Tian, Yun (Shanghai Normal University. Department of Mathematics)

Date:	2018
Abstract:	In the integrability of polynomial differential systems it is well known that the invariant algebraic curves play a relevant role. Here we will see that they can also play an important role with respect to limit cycles. In this paper, we study quadratic polynomial systems with an algebraic periodic orbit of degree 4 surrounding a center. We show that there exists only one family of such systems satisfying that an algebraic limit cycle of degree 4 can bifurcate from the period annulus of the mentioned center under quadratic perturbations.
Grants:	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:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Quadratic systems ; Quadratic vector fields ; Quadratic center ; Periodic orbit ; Limit cycle ; Bifurcation from center ; Cyclicity of the period annulus
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 28, Issue 11 (December 2018) , art. 1850145, ISSN 1793-6551

DOI: 10.1142/S0218127418501456

Postprint 11 p, 796.2 KB

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