On some \(k\)-dimensional cyclic systems of difference equations
type: Item
instance of: scholarly article
title: On some \(k\)-dimensional cyclic systems of difference equations
zbMATH Open document ID: 1205.39011
DOI: 10.1155/2010/528648
author: Wanping Liu
author: Xiaofan Yang
author: Bratislav Iričanin
published in: Abstract and Applied Analysis
publication date: 2010-09-27T00:00:00Z
review text: Summary: Motivated by \textit{B. D. Iričanin} and \textit{S. Stević}'s paper [Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 13, No.~3--4, 499--507 (2006; Zbl 1098.39003)] in which for the first time some cyclic systems of difference equations were considered, we study here the global attractivity of some nonlinear \(k\)-dimensional cyclic systems of higher-order difference equations. To do this, we use the transformation method from [\textit{K. S. Berenhaut} et al., Appl. Math. Lett. 20, No.~1, 54--58 (2007; Zbl 1131.39006); and \textit{K. S. Berenhaut} and \textit{S. Stević}, J. Math. Anal. Appl. 326, No.~2, 940--944 (2007; Zbl 1112.39002)]. The main results in this paper also extend our recent results in the work of [\textit{W. Liu} and \textit{X. Yang}, The global behavior of two higher-order symmetric recursive equations (2010) in press).
Mathematics Subject Classification ID: 39A22
zbMATH DE Number: 5791628
Wikidata QID: Q58649868
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2010/528648
OpenAlex ID: W2045740309
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: The global attractivity of a higher order rational difference equation
cites work: Q5479067
cites work: Global asymptotic behavior of positive solutions on the system of rational difference equations \(x_{n+1}=1+x_ n/y_{n-m}, y_ {n+1}=1+y_ n/x_{n-m}\).
cites work: On two systems of difference equations
cites work: On the positive solutions of the system of rational difference equations \(x_{n+1}=1/y_{n - k}, y_{n+1}=y_{n}/x_{n - m}y_{n - m - k}\)
cites work: On the system of rational difference equations \(x_n=a/y_{n-3}\), \(y_n=by_{n-3}/x_{n-q}y_{n-q}\)
cites work: On the behavior of the solutions of a system of two nonlinear difference equations.
cites work: Invariants for systems of two nonlinear difference equations
cites work: Linear difference equations mod 2 with applications to nonlinear difference equations1
cites work: Global stability of a rational symmetric difference equation
cites work: On a Class of Difference Equations with Strong Negative Feedback
cites work: Eventually constant solutions of a rational difference equation
cites work: Global asymptotic stability in some discrete dynamical systems
cites work: Global stability and asymptotics of some classes of rational difference equations
cites work: Asymptotics of some classes of higher-order difference equations
cites work: Existence of nontrivial solutions of a rational difference equation
cites work: Nontrivial solutions of a higher-order rational difference equation
cites work: Global stability of some symmetric difference equations
cites work: Stability of a generalized Putnam equation
cites work: Global asymptotic stability of a family of difference equations
description: scientific article; zbMATH DE number 5791628