Convergence and ultimate bounds of solutions of the nonautonomous Volterra-Lotka competition equations
type: Item
instance of: scholarly article
title: Convergence and ultimate bounds of solutions of the nonautonomous Volterra-Lotka competition equations
zbMATH Open document ID: 0648.34037
DOI: 10.1016/0022-247X(87)90116-8
author: Shair Ahmad
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: The author considers the nonautonomous system of differential equations \[ u'(t)=u(t)(a(t)-b(t)u(t)-c(t)v(t)) \] \[ v'(t)=v(t)(d(t)-e(t)u(t)- f(t)v(t)) \] where the functions a,...,f are assumed to be continuous and bounded above and below by positive constants on some half-infinite interval \(t_ 0\leq t<+\infty\). He shows that there is a solution \(col(u_ 0(t),v_ 0(t))\) for which the inequalities \(0<s_ 1\leq u_ 0(t)\leq r_ 1\), \(0<r_ 2\leq v_ 0(t)\leq s_ 2\) hold for \(t_ 0\leq t<+\infty\). If there are two solutions of that kind then their difference tends to zero as \(t\to +\infty\).
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 4057968
zbMATH Keywords: first order differential equation
MaRDI profile type: Publication
cites work: An application of topological degree to the periodic competing species problem
cites work: Q5533446
cites work: Q3895297
cites work: Exchange of equilibria in two species Lotka-Volterra competition models
cites work: Global asymptotic stability in a periodic Lotka-Volterra system
description: scientific article; zbMATH DE number 4057968