Pattern formation in a bistable ionic reaction-diffusion system
type: Item
instance of: scholarly article
title: Pattern formation in a bistable ionic reaction-diffusion system
zbMATH Open document ID: 0569.92030
author: H. Malchow
published in: Journal of Non-Equilibrium Thermodynamics
publication date: 1985-01-01T00:00:00Z
review text: The appearance of spatial inhomogeneous stationary solutions in a bistable three-component reaction-diffusion system with charged reactants is considered. The concept of ambipolar diffusion by Nernst and Schottky is used as an approximation. It is shown that the reaction system can be transformed to a Lotka-Volterra system. Conditions for bistability, oscillations, and time-independent Turing structures are derived. An inhomogeneous substance distribution is given analytically using the methods of bifurcation theory. The significance of ion patterns in biology and chemistry is emphasized.
Mathematics Subject Classification ID: 92Exx
Mathematics Subject Classification ID: 92C05
Mathematics Subject Classification ID: 80A30
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 3910214
zbMATH Keywords: pattern formation
zbMATH Keywords: ionic reaction models
zbMATH Keywords: spatial inhomogeneous stationary solutions
zbMATH Keywords: bistable three-component reaction-diffusion system
zbMATH Keywords: charged reactants
zbMATH Keywords: ambipolar diffusion
zbMATH Keywords: Lotka-Volterra system
zbMATH Keywords: bistability
zbMATH Keywords: oscillations
zbMATH Keywords: time-independent Turing structures
zbMATH Keywords: inhomogeneous substance distribution
zbMATH Keywords: bifurcation
zbMATH Keywords: ion patterns
MaRDI profile type: Publication
full work available at URL: jnet.1985.10.1.15
OpenAlex ID: W2086632437
cites work: Stochastic Bifurcations in a Bistable Reaction‐Diffusion System with Neumann Boundary Conditions
cites work: A bifurcation analysis of pattern formation in a diffusion governed morphogenetic field
DOI: 10.1515/JNET.1985.10.1.15
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description: scientific article; zbMATH DE number 3910214