Mathematical analysis of an activation-inhibition system in a discrete field
type: Item
instance of: scholarly article
title: Mathematical analysis of an activation-inhibition system in a discrete field
zbMATH Open document ID: 0554.92001
DOI: 10.1016/0025-5564(85)90075-6
published in: Mathematical Biosciences
publication date: 1985-01-01T00:00:00Z
review text: The activation-inhibition model of \textit{H. Meinhardt} and \textit{A. Gierer} [see J. Theor. Biol. 85, 429-450 (1980)] is investigated in the particular case of a stringlike set of cells. This reaction-diffusion system is considered, from a topical point of view, as a nonautonomous dynamic system which rules the behavior of each cell. It was shown that, when no diffusion occurs, this system can have either no or one or two stable steady states. The effect of intercellular exchanges on the existence and stability of these steady states is studied, so as to apply this model to the investigation of the branching of a filamentous lower plant.
Mathematics Subject Classification ID: 92B05
Mathematics Subject Classification ID: 92D15
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 3883983
zbMATH Keywords: topical analysis
zbMATH Keywords: morphogenesis
zbMATH Keywords: activation-inhibition model
zbMATH Keywords: stringlike set of cells
zbMATH Keywords: reaction-diffusion system
zbMATH Keywords: nonautonomous dynamic system
zbMATH Keywords: stable steady states
zbMATH Keywords: intercellular exchanges
zbMATH Keywords: branching of a filamentous lower plant
author: Christian Briere
MaRDI profile type: Publication
full work available at URL: 0025-5564(85)90075-6
OpenAlex ID: W1967078246
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cites work: Analytical treatment of pattern formation in the Gierer-Meinhardt model of morphogenesis
cites work: Pattern formation in morphogenesis. Analytical treatment of the Gierer- Meinhardt model on a sphere
cites work: Q5619740
description: scientific article; zbMATH DE number 3883983