The global attractivity of a higher order rational difference equation
type: Item
instance of: scholarly article
title: The global attractivity of a higher order rational difference equation
zbMATH Open document ID: 1112.39002
author: Stevo Stević
author: Kenneth S. Berenhaut
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-02-14T00:00:00Z
review text: Concerning the difference equation \(y_n= f(y_{n-k}, y_{n-1},y_{n-m})\) with \[ f(x,y,z)= (xyz+ x+ y+ z)/(1+ xy+ xz+ yz) \] and \(1\leq k\leq 1\leq m\) the authors prove that every positive solution converges to \(1\). Moreover, for small \(k\), \(l\), \(m\) the semi-cycle structure of the solutions is pointed out.
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A20
zbMATH DE Number: 5125945
zbMATH Keywords: rational difference equation
zbMATH Keywords: stability
zbMATH Keywords: symmetry
zbMATH Keywords: semi-cycles
zbMATH Keywords: positive solution
reviewed by: Lothar Berg
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.02.087
OpenAlex ID: W2017702502
cites work: The global attractivity of the rational difference equation $y_{n}=1+\frac{y_{n-k}}{y_{n-m}}$
cites work: Progress Report on Rational Difference Equations
cites work: Q3137926
cites work: Qualitative properties for a fourth-order rational difference equation
cites work: Global behavior for a fourth-order rational difference equation
cites work: Two rational recursive sequences
DOI: 10.1016/J.JMAA.2006.02.087
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description: scientific article; zbMATH DE number 5125945