Separatrices of competition-diffusion equations
type: Item
instance of: scholarly article
title: Separatrices of competition-diffusion equations
zbMATH Open document ID: 0858.35061
author: Hirokazu Ninomiya
published in: Journal of Mathematics of Kyoto University
publication date: 1996-07-01T00:00:00Z
review text: The Lotka-Volterra competition model with diffusion \[ u_t=d_1u_{xx}+ u(m_1-c_{11}u-c_{12}v), \quad v_t=d_2v_{xx}+ v(m_1-c_{21}v-c_{22}u) \qquad (0<x<1,\;t>0), \] under Neumann boundary conditions is investigated. The constants in the equations are set such that the system has two stable spatially constant equilibria contained on the boundary of the first orthant in the \(u\), \(v\) plane. The author describes the separatrix of the basins of attraction of these equilibria near a third (unstable) equilibrium and discusses conditions on the initial state that determine the asymptotic state of the solution as \(t\to\infty\).
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 880142
zbMATH Keywords: Lotka-Volterra system
zbMATH Keywords: extinction
zbMATH Keywords: separatrix
reviewed by: Peter Poláčik
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250518709
OpenAlex ID: W1754536732
DOI: 10.1215/KJM/1250518709
description: scientific article; zbMATH DE number 880142