Computing centre conditions for certain cubic systems
type: Item
instance of: scholarly article
title: Computing centre conditions for certain cubic systems
zbMATH Open document ID: 0754.65072
DOI: 10.1016/0377-0427(92)90188-4
published in: Journal of Computational and Applied Mathematics
publication date: 1993-01-16T00:00:00Z
review text: Necessary and sufficient conditions are presented for the origin to be a centre for cubic systems of the form \(\dot x=y\), \(\dot y=-x+A_ 1x^ 2+xy+A_ 3y^ 2+A_ 4x^ 3+A_ 5x^ 2y+A_ 6xy^ 2+A_ 7y^ 3\). The orbits are emphasized as the level curves of some functions. Extensive use of the computer algebra system REDUCE is involved. These conditions characterize the persistent centres (i.e. centres that are not destroyed by all perturbations within the given class of systems). The authors conjecture that there are no nonpersistent centres for the given cubic systems.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 89623
zbMATH Keywords: nonlinear differential equations
zbMATH Keywords: cubic systems
zbMATH Keywords: centre conditions
zbMATH Keywords: REDUCE
zbMATH Keywords: Hilbert's sixteenth problem
zbMATH Keywords: limit cycles
zbMATH Keywords: computer algebra
zbMATH Keywords: persistent centres
author: Noel G. Lloyd
author: Jane M. Pearson
reviewed by: Valeriu Prepeliţă
describes a project that uses: REDUCE
MaRDI profile type: Publication
full work available at URL: 0377-0427(92)90188-4
OpenAlex ID: W1965947648
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description: scientific article; zbMATH DE number 89623