Patterns in square arrays of coupled cells
type: Item
instance of: scholarly article
title: Patterns in square arrays of coupled cells
zbMATH Open document ID: 0889.34033
author: David Gillis
author: Martin Golubitsky
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-06-01T00:00:00Z
review text: The authors investigate discretizations of reaction-diffusion equations in a square lattice. This can be viewed as a system of oscillators which are coupled identical in all directions. Embedding the \(n\times n\)-square into a \(2n\times 2n\)-square enables the treatment of periodic boundary conditions and the investigation of hidden symmetries. The bifurcations of the symmetric steady state solutions of the ordinary differential equations are investigated with the help of the equivariant branching lemma by Vanderbauwhede. Several figures illustrate the various types of symmetric solutions nicely. Finally, stability is investigated and the Brusselator is considered as an example.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 35B32
zbMATH DE Number: 1031585
zbMATH Keywords: reaction-diffusion equations
zbMATH Keywords: equivariant dynamical systems
zbMATH Keywords: equivariant branching lemma
zbMATH Keywords: bifurcation theory
reviewed by: Karin Gatermann
MaRDI profile type: Publication
OpenAlex ID: W2117734515
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DOI: 10.1006/JMAA.1997.5347
description: scientific article; zbMATH DE number 1031585