The global attractivity of difference equations of nonincreasing nonlinearities with applications.
type: Item
instance of: scholarly article
title: The global attractivity of difference equations of nonincreasing nonlinearities with applications.
zbMATH Open document ID: 1036.39008
DOI: 10.1016/S0898-1221(03)00035-X
publication date: 2003-12-14T00:00:00Z
review text: The author studies the global attractivity of the unique positive equilibrium of the equation \(x_{n+1}=g(x_{n-k_1},x_{n-k_2},\dots,x_{n-k_m}),\;n=0,1,2,\dots\), where \(g\) is a nonincreasing continuous function in each of its arguments and the \(k\) are positive integers. The obtained results extend previous ones by \textit{M. Arciero, G. Ladas}, and \textit{S. W. Schultz} in [Georgian Math. J. 1, 229--233 (1994; Zbl 0808.39003)]. An application is made for the discrete Clark model \(x_{n+1}=\alpha x_n+f(x_{n-k})\) and the rational recursive sequence \(x_{n+1}=(a+bx_n)/(A+x_{n-1})\).
reviewed by: Nguyen Van Minh
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 37E05
zbMATH DE Number: 2017227
zbMATH Keywords: global attractivity
zbMATH Keywords: Clark model
zbMATH Keywords: difference equations
zbMATH Keywords: positive equilibrium
author: Hassan A. El-Morshedy
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2017227