On the global attractivity of systems of nonlinear difference equations
type: Item
instance of: scholarly article
title: On the global attractivity of systems of nonlinear difference equations
zbMATH Open document ID: 1030.39022
DOI: 10.1016/S0096-3003(01)00338-1
author: H. Y. Mohamed
author: H. M. El-Owaidy
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The global atractivity of the positive solutions of two systems of nonlinear difference equations, \(X_{n+1}=AX_n+F(X_{n-k})\), with \(A\) an \(m\times m\) matrix and \(F\in C[[0,\infty)^m,(0,\infty)^m]\), and \(X_{n+1}=G(X_n,\dots,X_{n-k})\), \(n=0,1,\dots,\) with \(G\in C[(0,\infty)^{m(k+1)},(0,\infty)^m]\) is studied. The authors give some sufficient conditions on the spectral radius of \(A\) and in the monotony properties of the functions \(F\) and \(G\) to ensure that every positive solution of such problems is attracted to \(\overline X\), with \(\overline X\) the unique positive equilibrium of the two studied systems.
reviewed by: Alberto Cabada
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 1861351
zbMATH Keywords: global attractivity
zbMATH Keywords: system of nonlinear difference equations
zbMATH Keywords: positive solutions
zbMATH Keywords: positive equilibrium
MaRDI profile type: Publication
cites work: The dynamics of some discrete population models
cites work: Q3137926
full work available at URL: s0096-3003(01)00338-1
OpenAlex ID: W1987664756
description: scientific article; zbMATH DE number 1861351