Unstable subsystems cause Turing instability
type: Item
instance of: scholarly article
title: Unstable subsystems cause Turing instability
zbMATH Open document ID: 1247.35060
author: Atsushi Anma
author: Kunimochi Sakamoto
author: Tohru Yoneda
published in: Kodai Mathematical Journal
publication date: 2012-08-29T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.kmj/1341401049
reviewed by: E. Ahmed
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35Q92
zbMATH DE Number: 6073745
zbMATH Keywords: 3-dimensional Turing instability
zbMATH Keywords: unstable subsystems
zbMATH Keywords: reaction diffusion equations
MaRDI profile type: Publication
OpenAlex ID: W2084736067
DOI: 10.2996/KMJ/1341401049
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review text: From the authors' abstract: ``We study Turing instabilities in 3-component reaction-diffusion systems. The existence of a complementary pair of stable-unstable subsystems always gives rise to Turing instability for suitable diagonal diffusion matrices. There are two types of Turing instability, one called steady instability and the other wave instability. To determine which of the two types of instability actually occurs, easily verifiable conditions on unstable subsystems are given. A complementary pair of unstable-unstable subsystems in a stable full system also leads to steady instability. Our results give a perspective to the rich variety and complexity of pattern dynamics in 3-component systems of reaction-diffusion equations at the onset.''NEWLINENEWLINEThe paper is clear and well written on an important topic but the references are a bit outdated.
description: scientific article; zbMATH DE number 6073745