Global asymptotic stability for two recursive difference equations.
type: Item
instance of: scholarly article
title: Global asymptotic stability for two recursive difference equations.
zbMATH Open document ID: 1044.39006
DOI: 10.1016/S0096-3003(03)00286-8
author: Xianyi Li
author: Deming Zhu
published in: Applied Mathematics and Computation
publication date: 2004-03-14T00:00:00Z
review text: The authors study the global asymptotic stability of the following two recursive difference equations \[ x_{n+1}=\frac{x_nx_{n-1}+x_{n-1}+a}{x_n+x_{n-1}x_{n-2}+a},\text{ } n=0,1,2,..., \] and \[ x_{n+1}=\frac{x_{n-1}+x_nx_{n-2}+a}{x_nx_{n-1}+x_{n-2}+a},\text{ } n=0,1,2,..., \] where \(a\in [0,\infty )\) and the initial values \(x_{-2},x_{-1},x_0\in (0,\infty )\). They prove that the positive equilibria of the two recursive difference equations are global asymptotically stable if \(a\in [0,\infty )\).
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A20
zbMATH DE Number: 2055869
zbMATH Keywords: recursive difference equation
zbMATH Keywords: global asymptotic stability
zbMATH Keywords: semicycle
reviewed by: Wan-Tong Li
MaRDI profile type: Publication
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full work available at URL: s0096-3003(03)00286-8
OpenAlex ID: W2025205926
description: scientific article; zbMATH DE number 2055869