Eventually periodic solutions of a max-type system of difference equations of higher order
type: Item
instance of: scholarly article
title: Eventually periodic solutions of a max-type system of difference equations of higher order
zbMATH Open document ID: 1417.39046
DOI: 10.1155/2018/8467682
author: Guangwang Su
author: Taixiang Sun
author: Bin Qin
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-20T00:00:00Z
review text: Summary: We study in this paper the following max-type system of difference equations of higher order: \(x_n=\max\{A,y_{n-k}/x_{n-1}\}\) and \(y_n=\max\{B,x_{n-k}/y_{n-1}\}\), \(n\in\{0,1,2,\dots\}\), where \(A\geq B>0\), \(k\geq1\), and the initial conditions \(x_{-k},y_{-k},x_{-k+1},y_{-k+1},\dots,x_{-1},y_{-1}\in(0,+\infty)\). We show that (1) if \(AB>1\), then every solution of the above system is periodic with period 2 eventually. (2) If \(AB=1>B\), then every solution of the above system is periodic with period \(2k\) or 2 eventually. (3) If \(A=B=1\) or \(AB<1\), then the above system has a solution which is not periodic eventually.
Mathematics Subject Classification ID: 39A23
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 7026704
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/8467682
OpenAlex ID: W2800302557
cites work: On a system of difference equations with maximum
cites work: Solutions of a max-type system of difference equations
cites work: On the solutions of a system of difference equations with maximum
cites work: On the solutions of a max-type difference equation system
cites work: Q5400516
cites work: Boundedness character of positive solutions of a max difference equation
cites work: Q3114957
cites work: On a class of nonautonomous max-type difference equations
cites work: Dynamics of the max-type difference equation \(x_{n+1} =\max\left\{\frac{A}{x_n},x_{n-k}\right\}\)
cites work: Global convergence of max-type equations
cites work: On a generalized max-type difference equation from automatic control theory
cites work: Q3105527
cites work: Product-type system of difference equations of second-order solvable in closed form
cites work: Q5251024
cites work: Q5251001
cites work: Global behavior of the max-type difference equation \(x_{n+1}=\max\{1/x_{n},A_{n}/x_{n - 1}\}\)
cites work: Dynamics of the max-type difference equation \({x_n=\max\{\frac{1}{x_{n-m}},\frac{A_n}{x_{n-r}}\}}\)
cites work: Eventually periodic solutions of a max-type equation
description: scientific article; zbMATH DE number 7026704