Global aspect of steady-states for competitive-diffusive systems with homogeneous Dirichlet conditions
type: Item
instance of: scholarly article
title: Global aspect of steady-states for competitive-diffusive systems with homogeneous Dirichlet conditions
zbMATH Open document ID: 0588.35050
DOI: 10.1016/0167-2789(84)90002-2
author: Masayuki Ito
published in: Physica D
publication date: 1984-01-01T00:00:00Z
review text: A coupled pair of diffusion equations in one space variable is considered under Lotka-Volterra dynamics and homogeneous Dirichlet boundary conditions. Using primarily bifurcation theory methods and linearized stability analysis the author obtains a fairly complete (although not a totally complete) description of the existence and stability properties of nonnegative and positive stationary solutions as they depend upon the two diffusion coefficients. Of particular interest is the demonstration (analytically and numerically) of the possible existence of stable positive stationary solutions for values of the interaction coefficients which allow no positive equilibrium solutions for the nondiffusion Lotka- Volterra equations.
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35G30
zbMATH DE Number: 3944399
zbMATH Keywords: coupled pair of diffusion equations
zbMATH Keywords: Lotka-Volterra dynamics
zbMATH Keywords: bifurcation theory
zbMATH Keywords: linearized stability analysis
zbMATH Keywords: positive stationary solutions
zbMATH Keywords: interaction coefficients
zbMATH Keywords: equilibrium solutions
reviewed by: J. M. Cushing
MaRDI profile type: Publication
full work available at URL: 0167-2789(84)90002-2
OpenAlex ID: W1963976531
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description: scientific article; zbMATH DE number 3944399