Dynamics of a higher-order nonlinear difference equation
type: Item
instance of: scholarly article
title: Dynamics of a higher-order nonlinear difference equation
zbMATH Open document ID: 1198.39030
DOI: 10.1155/2010/534947
author: Guo-Mei Tang
author: Lin-Xia Hu
author: Xiumei Jia
published in: Discrete Dynamics in Nature and Society
publication date: 2010-09-29T00:00:00Z
full work available at URL: https://eudml.org/doc/228413
review text: Summary: We consider the higher-order nonlinear difference equation \[ x_{n+1}=\frac{\alpha +x_{n}}{A+Bx_{n}+x_{n - k}},\quad n=0,1,\dots, \] where the parameters are positive real numbers and the initial conditions \(x_{ - k},\dots ,x_{0}\) are nonnegative real numbers, \(k\geq 2\). We investigate the periodic character, the invariant intervals, and the global asymptotic stability of all positive solutions of the abovementioned equation. We show that the unique equilibrium of the equation is globally asymptotically stable under certain conditions.
Mathematics Subject Classification ID: 39A30
Mathematics Subject Classification ID: 39A22
Mathematics Subject Classification ID: 39A20
zbMATH DE Number: 5793497
zbMATH Keywords: rational difference equation
zbMATH Keywords: higher-order nonlinear difference equation
zbMATH Keywords: invariant intervals
zbMATH Keywords: positive solutions
zbMATH Keywords: equilibrium
MaRDI profile type: Publication
OpenAlex ID: W1970525472
Wikidata QID: Q58650830
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description: scientific article; zbMATH DE number 5793497