Center problem and bifurcation behavior for a class of quasi analytic systems
type: Item
instance of: scholarly article
title: Center problem and bifurcation behavior for a class of quasi analytic systems
zbMATH Open document ID: 1213.37079
author: Haibo Chen
author: Chaoxiong Du
author: Yirong Liu
published in: Applied Mathematics and Computation
publication date: 2011-02-02T00:00:00Z
review text: The authors discuss a class of quasi-analytic systems depending on a parameter from the viewpoint of determining whether a nondegenerate critical point is a center or a weak focus (the center-focus problem) and whether or not the limit cycles bifurcate. A reduction theorem is obtained by means of a formal series expansion, being shown that the origin (or the singular point at infinity) is a center (a isochronous center) if and only if the origin of an associated analytic system is a center (an isochronous center). As an example, the center-focus and bifurcation problem of a class of quasi-analytic cubic systems is studied, a recursive formula to determine the generalized focal values being obtained.
reviewed by: Paul Georgescu
Mathematics Subject Classification ID: 37G15
zbMATH DE Number: 5843691
zbMATH Keywords: quasi analytic planar differential system
zbMATH Keywords: generalized focal values
zbMATH Keywords: limit cycles
zbMATH Keywords: center
zbMATH Keywords: isochronous center
MaRDI profile type: Publication
full work available at URL: j.amc.2010.11.018
OpenAlex ID: W2135263038
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DOI: 10.1016/J.AMC.2010.11.018
description: scientific article; zbMATH DE number 5843691