The effect of diffusion for the multispecies Lotka--Volterra competition model
type: Item
instance of: scholarly article
title: The effect of diffusion for the multispecies Lotka--Volterra competition model
zbMATH Open document ID: 1015.35039
DOI: 10.1016/S1468-1218(02)00066-4
author: Salomé Martínez
published in: Nonlinear Analysis. Real World Applications
publication date: 2003-05-14T00:00:00Z
review text: The paper studies the effect of diffusion in existence of non-constant steady states for the Lotke-Volterra competition-diffusion system with three species under Neumann boundary conditions. It is shown that two large diffusion rates prevent the appearance of non-constant steady states while if just one species diffuses fast non-constant equilibria may occur. Degree theory and bifurcation techniques are the main tools in establishing existence.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35J55
zbMATH DE Number: 1910227
zbMATH Keywords: non-constant steady states
zbMATH Keywords: competitive system
zbMATH Keywords: three species
zbMATH Keywords: Neumann boundary conditions
zbMATH Keywords: two large diffusion rates
zbMATH Keywords: degree theory
zbMATH Keywords: bifurcation techniques
MaRDI profile type: Publication
cites work: Decay to Uniform States in Ecological Interactions
cites work: Q3254327
cites work: Uniqueness and nonuniqueness of coexistence states in the lotka‐volterra competition model
cites work: The diffusive Lotka-Volterra system with three species can have a stable non-constant equilibrium solution
cites work: The spatial homogeneity of stable equilibria of some reaction-diffusion systems on convex domains
cites work: Diffusion, self-diffusion and cross-diffusion
cites work: Q4774620
cites work: Asymptotic behavior of a competition—diffusion system in population dynamics
full work available at URL: s1468-1218(02)00066-4
OpenAlex ID: W1974870144
description: scientific article; zbMATH DE number 1910227