On the heterogeneity of reaction-diffusion generated pattern
type: Item
instance of: scholarly article
title: On the heterogeneity of reaction-diffusion generated pattern
zbMATH Open document ID: 0616.92001
DOI: 10.1007/BF02459700
author: Christoph Berding
published in: Bulletin of Mathematical Biology
publication date: 1987-01-01T00:00:00Z
review text: Several current reaction-diffusion mechanisms have been proposed as models for morphogenesis in the \textit{A. M. Turing} [Philos. Trans. R. Soc. Lond. B 237, 37-72 (1952)] sense. We introduce and exploit a quantity, we have termed heterogeneity, which allows us to elaborate the differences between the various models with regard to spatial pattern formation. It is shown that this quantity provides a concise view for the comparison of theoretical models with experimental observations. Two model mechanisms are treated explicitly both for linear and for biased diffusion.
Mathematics Subject Classification ID: 92B05
Mathematics Subject Classification ID: 35K99
Mathematics Subject Classification ID: 92D15
Mathematics Subject Classification ID: 92F05
zbMATH DE Number: 3999721
zbMATH Keywords: linear diffusion
zbMATH Keywords: reaction-diffusion mechanisms
zbMATH Keywords: morphogenesis
zbMATH Keywords: heterogeneity
zbMATH Keywords: spatial pattern formation
zbMATH Keywords: biased diffusion
MaRDI profile type: Publication
Wikidata QID: Q52610736
cites work: Q4077009
cites work: Bifurcation analysis of nonlinear reaction diffusion equations I. Evolution equations and the steady state solutions
cites work: Bifurcation, stability diagrams, and varying diffusion coefficients in reaction-diffusion equations
cites work: Q4045366
cites work: Large Time Behavior of Solutions of Systems of Nonlinear Reaction-Diffusion Equations
cites work: Q3236921
cites work: Singular Secondary Bifurcation
cites work: Q4051967
cites work: Synergetics. An introduction. Nonequilibrium phase transitions and self- organization in physics, chemistry and biology. 2nd enl. ed
cites work: Morphogen pattern formation and development in growth
cites work: Q4158861
cites work: Concentration-dependent diffusion coefficient and dissipative structures
cites work: Q4182303
cites work: Solutions to systems of nonlinear reaction-diffusion equations
cites work: Topics in stability and bifurcation theory
cites work: Q5732663
cites work: Q4746129
cites work: The chemical basis of morphogenesis
full work available at URL: https://doi.org/10.1007/bf02459700
OpenAlex ID: W4245615076
description: scientific article; zbMATH DE number 3999721