The asymptotic stability of \(x_{n+1}-ax_ n+bx_{n-k}=0\)
type: Item
instance of: scholarly article
title: The asymptotic stability of \(x_{n+1}-ax_ n+bx_{n-k}=0\)
zbMATH Open document ID: 0842.39004
author: Spiridon A. Kuruklis
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-08-11T00:00:00Z
review text: For linear difference equations of the form \[ x_{n+1}= ax_n+ bx_{n-k}, \qquad n\in \mathbb{N}\cup \{0\} \] necessary and sufficient conditions for the asymptotic stability are presented in terms of the real coefficients \(a\), \(b\) and the delay \(k\in \mathbb{N}\cup \{0\}\). The proof of the main result is based on a careful analysis of the dependence of the roots of the characteristic polynomial on the parameters \(a\), \(b\) and \(k\).
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 720396
zbMATH Keywords: linear difference equations
zbMATH Keywords: asymptotic stability
zbMATH Keywords: delay
reviewed by: Bernd Aulbach
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1457
OpenAlex ID: W2088979499
DOI: 10.1006/JMAA.1994.1457
description: scientific article; zbMATH DE number 720396