Diffusion effect on stability of Lotka-Volterra models
type: Item
instance of: scholarly article
title: Diffusion effect on stability of Lotka-Volterra models
zbMATH Open document ID: 0613.92025
DOI: 10.1007/BF02462325
author: Yasuhiro Takeuchi
published in: Bulletin of Mathematical Biology
publication date: 1986-01-01T00:00:00Z
review text: This paper analyses the diffusion effect on stability in Lotka-Volterra systems for a patch-type environment. Applying the extended stability theorem of LaSalle, some classes of patches for which the diffusion does not affect the system's stability are drawn. Further, complicated dynamical behaviours in two-prey, one-predator diffusion models are given when the patch does not belong to the above classes.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 34D99
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 3993368
zbMATH Keywords: diffusion effect on stability
zbMATH Keywords: Lotka-Volterra systems
zbMATH Keywords: patch-type environment
zbMATH Keywords: extended stability theorem of LaSalle
zbMATH Keywords: two-prey, one- predator diffusion models
Wikidata QID: Q52653384
MaRDI profile type: Publication
cites work: Persistence and extinction in Lotka-Volterra reaction-diffusion equations
cites work: Convergence to Homogeneous Equilibrium State for Generalized Volterra–Lotka Systems with Diffusion
cites work: Some generalizations of positive definiteness and monotonicity
cites work: Global stability in Lotka-Volterra systems with diffusion
cites work: Dynamics of a single species in a spatially varying environment: The stabilizing role of high dispersal rates
cites work: Q4106027
cites work: Q4070658
cites work: Q3856484
cites work: Solutions to systems of nonlinear reaction-diffusion equations
cites work: Effects of diffusion on the stability of the equilibrium in multi-species ecological systems
cites work: Solutions to certain classes of linearized reaction-diffusion equations
cites work: Global stability in generalized Lotka-Volterra diffusion systems
cites work: The existence of globally stable equilibria of ecosystems of the generalized Volterra type
cites work: Existence of stable equilibrium point for dynamical systems of Volterra type
cites work: Stable equilibrium of systems of generalized Volterra type
cites work: Existence and bifurcation of stable equilibrium in two-prey, one-predator communities
cites work: The stability of generalized Volterra equations
full work available at URL: https://doi.org/10.1007/bf02462325
OpenAlex ID: W2010668974
description: scientific article; zbMATH DE number 3993368