Global asymptotic stability in a rational recursive sequence
type: Item
instance of: scholarly article
title: Global asymptotic stability in a rational recursive sequence
zbMATH Open document ID: 1071.39018
author: Xiaofan Yang
author: D. J. Evans
author: Graham M. Megson
author: Hong-Jian Lai
published in: Applied Mathematics and Computation
publication date: 2005-01-17T00:00:00Z
review text: The global stability of the difference equation \[ x_{n}=\frac{a+bx_{n-1}+cx_{n-1}^2}{d-x_{n-2}}, \quad n=1,2,\dots \] where \(a,b\geq 0\) and \(c,d>0\) is studied. It is shown that one nonnegative equillibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive solution of the equation in the basin exponentially converges to the attractor.
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A20
zbMATH DE Number: 2128813
zbMATH Keywords: rational difference equation
zbMATH Keywords: Recursive sequence
zbMATH Keywords: Equilibrium
zbMATH Keywords: Global attractor
zbMATH Keywords: Basin
zbMATH Keywords: Exponential convergence
zbMATH Keywords: positive solution
reviewed by: Ioannis P. Stavroulakis
MaRDI profile type: Publication
full work available at URL: j.amc.2003.10.010
OpenAlex ID: W2099164657
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DOI: 10.1016/J.AMC.2003.10.010
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description: scientific article; zbMATH DE number 2128813