Discrete-time versus continuous-time models of neural networks
type: Item
instance of: scholarly article
title: Discrete-time versus continuous-time models of neural networks
zbMATH Open document ID: 0760.92001
DOI: 10.1016/0022-0000(92)90038-K
author: Xin Wang
author: Edward K. Blum
published in: Journal of Computer and System Sciences
publication date: 1993-01-16T00:00:00Z
review text: This paper considers the question of when a discretized version of a continuous-time (CT) system will have the same dynamical behavior as the original continuous-time system. Following a review of the status of the problem, the authors proceed to consider the general case of asymptotic consistency of the CT model and its associated discrete-time (DT) model. Specifically, let the CT system be given by the autonomous system of ordinary differential equations \(\dot x=F(x)\) and the corresponding DT model defined by \[ x(k+1)=x(k)+hF(x(k)). \] Conditions are given under which the DT model and the CT model have the same stable and unstable subspaces. Next, this general result is applied to four specific neural network models: (i) feedforward networks; (ii) symmetric networks; (iii) anti-symmetric networks; and (iv) circulant networks. These results generalize a number of results from the neural network literature, including those of Grossberg and Hopfield.
Mathematics Subject Classification ID: 92B20
Mathematics Subject Classification ID: 68U20
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 34A99
Mathematics Subject Classification ID: 68T05
zbMATH DE Number: 90310
zbMATH Keywords: continuous-time models
zbMATH Keywords: numerical analysis
zbMATH Keywords: discrete-time models
zbMATH Keywords: asymptotic consistency
zbMATH Keywords: autonomous system
zbMATH Keywords: feedforward networks
zbMATH Keywords: symmetric networks
zbMATH Keywords: anti-symmetric networks
zbMATH Keywords: circulant networks
reviewed by: Kevin L. Moore
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 90310