On the limit cycles bifurcating from an ellipse of a quadratic center
type: Item
instance of: scholarly article
title: On the limit cycles bifurcating from an ellipse of a quadratic center
zbMATH Open document ID: 1325.34055
author: Jaume Llibre
author: Dana Schlomiuk
published in: Discrete and Continuous Dynamical Systems
publication date: 2014-12-03T00:00:00Z
review text: The problem under consideration is to determine the influence of invariant algebraic curves of planar polynomial differential systems bifurcation of limit cycles. It is shown that in the case of polynomial perturbations of such systems algebraic invariant curves can generate algebraic limit cycles. By using the inverse integrating factor the authors prove that a perturbation of any quadratic system with an invariant ellipse surrounding a center within the class of quadratic systems provides the existence at least one 1-parameter family of such systems having a limit cycle bifurcating from the ellipse.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C07
zbMATH DE Number: 6376351
zbMATH Keywords: quadratic systems
zbMATH Keywords: quadratic center
zbMATH Keywords: periodic orbit
zbMATH Keywords: limit cycle
zbMATH Keywords: bifurcation from center
zbMATH Keywords: cyclicity of the period annulus
zbMATH Keywords: inverse integrating factor
MaRDI profile type: Publication
full work available at URL: dcds.2015.35.1091
OpenAlex ID: W2080034437
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DOI: 10.3934/DCDS.2015.35.1091
description: scientific article; zbMATH DE number 6376351