A note on mutual stability
type: Item
instance of: scholarly article
title: A note on mutual stability
zbMATH Open document ID: 0954.39006
DOI: 10.1016/S0960-0779(98)00124-6
author: Xiao-Song Yang
published in: Chaos, Solitons and Fractals
publication date: 1999-11-29T00:00:00Z
review text: The author in this short note discusses the problem of mutual stability of solutions to two difference equations of the type \[ x(k+1)=f \bigl(x(k), k\bigr) \] and \[ y(k+1)= g\bigl(y(k), k\bigr). \] Any two solutions \(x (k)= x(k,x_0)\) and \(y(k)= y(k,y_0)\) \((k\in\mathbb{Z}^+)\) with initial conditions \(x(0)= x_0\) and \(y(0)=y_0\) are said to be mutually stable, if for each \(\varepsilon > 0\) there exists a \(\delta>0\), such that \(\|x_0-y_0 \|\leq\delta\) implies \(\|x(k)-y(k) \|< \varepsilon\) for \(k\in\mathbb{Z}^+\).
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 1371677
zbMATH Keywords: mutual stability
zbMATH Keywords: difference equations
reviewed by: R. P. Agarwal
MaRDI profile type: Publication
cites work: Q4003305
cites work: A mathematical theory of synchronization by self-feedback
cites work: A note on mathematical aspects of drive-response type synchronization
cites work: Generalized synchronization in chaotic systems
cites work: Bubbling of attractors and synchronisation of chaotic oscillators
Wikidata QID: Q127120353
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description: scientific article; zbMATH DE number 1371677