On the difference equation \(x_{n+1}=\frac{\alpha x_{n-1}+\beta x_{n-k}}{Ax_{n-1}+Bx_{n-k}}\)
type: Item
instance of: scholarly article
title: On the difference equation \(x_{n+1}=\frac{\alpha x_{n-1}+\beta x_{n-k}}{Ax_{n-1}+Bx_{n-k}}\)
zbMATH Open document ID: 1154.39006
published in: Acta Mathematica Vietnamica
publication date: 2008-10-20T00:00:00Z
review text: The solutions of the difference equation in the title with positive coefficients and positive initial values are studied with respect to persistence and 2-periodicity. Moreover, conditions are given such that the equilibrium is locally asymptotically stable resp. a global attractor.
reviewed by: Lothar Berg
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A20
zbMATH DE Number: 5354281
zbMATH Keywords: rational difference equation
zbMATH Keywords: persistence
zbMATH Keywords: periodicity
zbMATH Keywords: stability
zbMATH Keywords: global attractor
author: E. M. Elabbasy
author: H. El-Metwally
author: E. M. Elsayed
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5354281