Global asymptotic behavior of a two-dimensional difference equation modelling competition
type: Item
instance of: scholarly article
title: Global asymptotic behavior of a two-dimensional difference equation modelling competition
zbMATH Open document ID: 1019.39006
DOI: 10.1016/S0362-546X(02)00294-8
author: Dean S. Clark
author: Mustafa R. S. Kulenovic
author: James F. Selgrade
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-11T00:00:00Z
review text: Consider the system of difference equations \[ x_{n+1}=\frac{x_n}{a+cy_n},\quad y_{n+1}=\frac{y_n}{b+dx_n}\quad n=0,1,\dots \quad (x_0\geq 0,\;y_0\geq 0)\tag{1} \] where \(a\) and \(b\) are in \((0,1),c\) and \(d\) are positive numbers. The global asymptotic behavior of solutions of (1) is investigated. The authors show that the stable manifold of (1) separates the positive quadrant into basins of attraction of two types of asymptotic behavior. An explicit equation for the stable manifold is obtained in the case where \(a=b\).
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39B05
zbMATH DE Number: 1880124
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: monotonicity
zbMATH Keywords: stability
zbMATH Keywords: stable manifold
zbMATH Keywords: system of difference equations
reviewed by: Fozi Dannan
MaRDI profile type: Publication
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full work available at URL: s0362-546x(02)00294-8
OpenAlex ID: W2076615094
description: scientific article; zbMATH DE number 1880124