On the rational recursive sequence \(x_{n+1}=Ax_{n}+Bx_{n-k}+\frac{\beta x_{n}+\gamma x_{n-k}}{cx_{n}+Dx_{n-k}}\)
type: Item
instance of: scholarly article
title: On the rational recursive sequence \(x_{n+1}=Ax_{n}+Bx_{n-k}+\frac{\beta x_{n}+\gamma x_{n-k}}{cx_{n}+Dx_{n-k}}\)
zbMATH Open document ID: 1204.39008
author: M. A. El-Moneam
author: Elsayed M. E. Zayed
published in: Acta Applicandae Mathematicae
publication date: 2010-07-24T00:00:00Z
full work available at URL: https://eudml.org/doc/38133
review text: The authors investigate some qualitative behavior of the solutions of the difference equation \[ x_{n+1}=Ax_{n}+Bx_{n-k}+\dfrac{\beta x_{n}+\gamma x_{n-k}}{Cx_{n}+Dx_{n-k} },\quad n=0,1,2,\dots, \] where the initial conditions \(x_{-k},\dots,x_{-1},x_{0}\) and the coefficients \(A,B,C,D,\beta,\gamma\) are positive real numbers, while \(k>0\) is an integer. Among other properties, they analyse the local and global stability, the boundedness, and the existence of periodic solutions. Finally, they consider some interesting examples.
Mathematics Subject Classification ID: 39A20
Mathematics Subject Classification ID: 39A22
Mathematics Subject Classification ID: 39A23
Mathematics Subject Classification ID: 39A30
zbMATH DE Number: 5760431
zbMATH Keywords: rational difference equations
zbMATH Keywords: prime period two solution
zbMATH Keywords: local asymptotic stability
zbMATH Keywords: global attractor
zbMATH Keywords: global stability
zbMATH Keywords: boundedness
reviewed by: Narcisa Apreutesei
MaRDI profile type: Publication
OpenAlex ID: W2008914198
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DOI: 10.1007/S10440-009-9545-Y
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description: scientific article; zbMATH DE number 5760431