Dynamics of \(x_{n+1}=\frac{x_{n-2k+1}}{x_{n-22k+1}+\alpha x_{n-2l}}\)
type: Item
instance of: scholarly article
title: Dynamics of \(x_{n+1}=\frac{x_{n-2k+1}}{x_{n-22k+1}+\alpha x_{n-2l}}\)
zbMATH Open document ID: 1114.39001
author: Reza Mazrooei-Sebdani
author: Mehdi Dehghan
published in: Applied Mathematics and Computation
publication date: 2007-03-12T00:00:00Z
review text: The paper deals with rational difference equation \[ x_{n+1} = \frac{x_{n-2k+1}}{x_{n-2k+1} + \alpha x_{n-2l}}, \;n= 0,1,\dots, \eqno(1) \] where \(k \in\{1,2,\dots\}, l \in\{0, 1,\dots\},\) and \(\alpha \neq 1.\) The authors prove that when \(\alpha < 1\) then every positive solution of (1) converges to the positive equilibrium \(\bar x = 1/(\alpha+1).\) When \(\alpha > 1\) eq. (1) possesses solutions that converges to the two-cycle \(\dots,0,1,0,1,\dots\). Some numerical examples are presented.
reviewed by: Victor I. Tkachenko
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A20
zbMATH DE Number: 5132935
zbMATH Keywords: rational difference equation
zbMATH Keywords: global stability
zbMATH Keywords: two cycle
zbMATH Keywords: boundedness
zbMATH Keywords: asymptotic stability
zbMATH Keywords: positive equilibrium
zbMATH Keywords: numerical examples
zbMATH Keywords: positive solution
MaRDI profile type: Publication
full work available at URL: j.amc.2006.07.068
OpenAlex ID: W162768077
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DOI: 10.1016/J.AMC.2006.07.068
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description: scientific article; zbMATH DE number 5132935