Global behavior of two families of nonlinear symmetric difference equations
type: Item
instance of: scholarly article
title: Global behavior of two families of nonlinear symmetric difference equations
zbMATH Open document ID: 1205.39012
DOI: 10.1155/2010/367492
author: Wanping Liu
author: Xiaofan Yang
author: Luxing Yang
published in: Discrete Dynamics in Nature and Society
publication date: 2010-09-29T00:00:00Z
full work available at URL: https://eudml.org/doc/223423
review text: Summary: We mainly investigate the global asymptotic stability and exponential convergence of positive solutions to two families of higher-order difference equations, one of which was recently studied in \textit{S. Stević}'s paper [Appl. Math. Comput. 216, No.~1, 179--186 (2010; Zbl 1193.39008)]. A new concise proof is given to a quite recent result by Stević and analogous parallel result of the other inverse equation, which extend related results of \textit{M. Aloqeili} [Appl. Math. Comput. 215, No.~3, 950--953 (2009; Zbl 1177.39019)], \textit{K. S. Berenhaut} and \textit{S. Stević} [J. Math. Anal. Appl. 326, No.~2, 940--944 (2007; Zbl 1112.39002)], and \textit{M. Liao} et al. [Adv. Difference Equ. 2009, Article ID 394635 (2009; Zbl 1166.39301)].
Mathematics Subject Classification ID: 39A22
zbMATH DE Number: 5793487
Wikidata QID: Q58650781
MaRDI profile type: Publication
OpenAlex ID: W1991925425
cites work: Global stability of a rational symmetric difference equation
cites work: The global attractivity of a higher order rational difference equation
cites work: The global attractivity of the rational difference equation \(y_n = \frac{y_{n-k}+y_{n-m}}{1+y_{n-k}y_{n-m}}\)
cites work: Quantitative bounds for the recursive sequence \(y_{n} + 1 = A + \frac {{y}_{n}}{{y}_{n-k}}\)
cites work: Q5703164
cites work: On the recursive sequence 𝑥_{𝑛+1}=\frac{𝐴}𝑥_{𝑛}+\frac{1}𝑥_{𝑛-2}
cites work: Dynamics of a class of higher order difference equations
cites work: Qualitative properties for a fourth-order rational difference equation
cites work: Global behavior for a fourth-order rational difference equation
cites work: Global asymptotic stability for two recursive difference equations.
cites work: Two rational recursive sequences
cites work: Global Asymptotic Stability in a Rational Equation*
cites work: On a conjecture for a higher-order rational difference equation
cites work: Global asymptotic behavior and boundedness of positive solutions to an odd-order rational difference equation
cites work: Nontrivial solutions of a higher-order rational difference equation
cites work: Existence of nontrivial solutions of a rational difference equation
cites work: Global stability and asymptotics of some classes of rational difference equations
cites work: Stability of solutions for a family of nonlinear difference equations
cites work: Global asymptotic stability of a higher order rational difference equation
cites work: Global attractivity for a family of nonlinear difference equations
cites work: Global behavior of a higher-order rational difference equation
cites work: Stability of a generalized Putnam equation
cites work: Global asymptotic stability of a family of difference equations
cites work: Boundedness character of a class of difference equations
cites work: On asymptotic behaviour of the difference equation \(x_{n+1} = \alpha+\frac{x_{n-1}^p}{x_n^p}\).
cites work: On a class of third-order nonlinear difference equations
cites work: Boundedness character of two classes of third-order difference equations(1
cites work: On the recursive sequence \(x_{n+1}=A+x_{n}^{p}/x_{n-1}^{p}\)
cites work: On the recursive sequence \(x_{n+1}=\frac{\alpha+\beta x_{n-k}}{f(x_n,\dots,x_{n-k+1})}\)
cites work: Linear difference equations mod 2 with applications to nonlinear difference equations1
cites work: Global stability of some symmetric difference equations
cites work: Global asymptotic stability in some discrete dynamical systems
cites work: Inclusion Theorems for Non-linear Difference Equations with Applications
cites work: Asymptotics of some classes of higher-order difference equations
cites work: Asymptotic behavior of a class of nonlinear difference equations
cites work: On monotone solutions of some classes of difference equations
cites work: On positive solutions of a (\(k+1\))th order difference equation
cites work: Q3634784
cites work: Q4456895
description: scientific article; zbMATH DE number 5793487