Robust stability of a class of neural networks with time delays
type: Item
instance of: scholarly article
title: Robust stability of a class of neural networks with time delays
zbMATH Open document ID: 0882.92002
DOI: 10.1007/BF02219053
published in: Journal of Dynamics and Differential Equations
publication date: 1998-03-10T00:00:00Z
review text: Neural networks are modelled by nonlinear ODE's with one or two constant delays. It is assumed that the linear part, centred on a static equilibrium, is dominant. The stability analysis is carried out by examining the eigenvalues (roots of quasipolynomials), and their dependence on parameters. The permissible change of the latter determines ``robustness''. This notion does not coincide with an analoguos notion introduced by Andronov and extended by Smale. The stability so determined is local. The possibility of small ``hard-type'' self-oscillations is not considered.
Mathematics Subject Classification ID: 92B20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1046322
zbMATH Keywords: local stability
zbMATH Keywords: linear dominance
zbMATH Keywords: roots of quasipolynomials
zbMATH Keywords: sensitivity to parameter changes
author: V. L. Kharitonov
author: Andrew D. B. Paice
reviewed by: Igor Gumowski
MaRDI profile type: Publication
cites work: Q5485394
cites work: Root locations of an entire polytope of polynomials: It suffices to check the edges
cites work: Stability in a model of a delayed neural network
cites work: Differential-difference equations
cites work: Robust stability for time-delay systems: the edge theorem and graphical tests
cites work: Q3356185
cites work: Neurons with graded response have collective computational properties like those of two-state neurons.
cites work: Robust stability of time-delay systems
cites work: The complex structured singular value
cites work: On the zeros of some transcendental functions
cites work: Finiteness results for sigmoidal “neural” networks
full work available at URL: https://doi.org/10.1007/bf02219053
OpenAlex ID: W1994406678
description: scientific article; zbMATH DE number 1046322