Higher order limit cycle bifurcations from non-degenerate centers
type: Item
instance of: scholarly article
title: Higher order limit cycle bifurcations from non-degenerate centers
zbMATH Open document ID: 1255.34041
author: Jaume Giné
published in: Applied Mathematics and Computation
publication date: 2012-08-19T00:00:00Z
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 6068322
zbMATH Keywords: Poincaré-Lyapunov constant
zbMATH Keywords: limit cycle
zbMATH Keywords: center problem
zbMATH Keywords: Gröbner basis
describes a project that uses: REDUCE
describes a project that uses: strudel
MaRDI profile type: Publication
full work available at URL: j.amc.2012.02.044
OpenAlex ID: W2089595622
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DOI: 10.1016/J.AMC.2012.02.044
review text: The paper is devoted to the computation of the Poincaré-Lyapunov constants and to the determination of their functionally independent number for the following systems NEWLINE\[NEWLINE \dot{x}=-y+P_n(x, y), \;\dot{y}=x+Q_n(x, y), NEWLINE\]NEWLINE where \(P_n\) and \(Q_n\) are homogeneous polynomials of degree \(n\). By means of center bifurcation, the author estimates the cyclicity of a unique singular point of focus-center type for different values of \(n\). The presented results are obtained by using the implementation worked out by C. Christopher which exploits Cartesian coordinates and the computer algebra system \texttt{Reduce}.
reviewed by: Alexander Grin
description: scientific article; zbMATH DE number 6068322