The stable coexistence of competing species on a renewable resource
type: Item
instance of: scholarly article
title: The stable coexistence of competing species on a renewable resource
zbMATH Open document ID: 0661.92021
DOI: 10.1016/0022-247X(89)90303-X
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: We consider a system of three autonomous ordinary differential equations modeling two competing species for a prey resource. We obtain a simple criterion in terms of the specific growth of the prey for there to be an asymptotically stable equilibrium. In a special case, we show that a Hopf bifurcation about this equilibrium could occur. In another special case we show that the interior equilibrium could be globally asymptotically stable. The results are illustrated by a numerical example.Finally it is shown that in the general case, not all competition models posess the properties described in this paper.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 4081364
zbMATH Keywords: local stability
zbMATH Keywords: global stability
zbMATH Keywords: autonomous ordinary differential equations
zbMATH Keywords: two competing species
zbMATH Keywords: prey resource
zbMATH Keywords: asymptotically stable equilibrium
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: numerical example
zbMATH Keywords: competition models
author: M. Farkas
author: H. I. Freedman
MaRDI profile type: Publication
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cites work: Q5569684
full work available at URL: 0022-247x(89)90303-x
OpenAlex ID: W1978480648
description: scientific article; zbMATH DE number 4081364