Invariant and attracting sets of Volterra difference equations with delays
type: Item
instance of: scholarly article
title: Invariant and attracting sets of Volterra difference equations with delays
zbMATH Open document ID: 1065.39021
DOI: 10.1016/S0898-1221(03)00104-4
publication date: 2004-08-06T00:00:00Z
review text: The asymptotic properties, stability, existence of invariant sets and estimation of the basin of attraction are important in the theories of differential, difference and delayed differential equations. In this paper the author develops techniques for determinig the invariant and attracting sets of Volterra difference equations with delay. In case of an equilibrium solution, the basin of attraction becomes the domain of attraction of the asymptotic stability of the system. Two examples are given.
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 37C15
Mathematics Subject Classification ID: 37C70
zbMATH DE Number: 2082236
zbMATH Keywords: invariant set
zbMATH Keywords: attracting set
zbMATH Keywords: delay systems
zbMATH Keywords: Volterra difference equations
zbMATH Keywords: asymptotic stability
author: Daoyi Xu
reviewed by: Ahmed Hegazi
MaRDI profile type: Publication
cites work: Q4039920
cites work: Existence and persistence of invariant manifolds for semiflows in Banach space
cites work: Infinite-dimensional dynamical systems in mechanics and physics.
cites work: Q3998731
cites work: Q4160745
cites work: Q4141027
cites work: Uniform asymptotic stability of abstract functional differential equations
cites work: Theory of difference equations: Numerical methods and applications
cites work: Q4033029
cites work: Asymptotic constancy of solutions of linear parabolic Volterra difference equations
cites work: Q4854839
cites work: Domain of attraction of nonlinear discrete systems with delays
cites work: A new Razumikhin theorem for delay difference equations
cites work: Asymptotic behavior of nonlinear difference equations with delays
cites work: Stability of difference Volterra equations: Direct Lyapunov method and numerical procedure
cites work: Stability criteria in terms of two measures for discrete systems
cites work: Periodicity and stability of linear Volterra difference systems
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 2082236