On global asymptotic stability of a class of nonlinear systems arising in neural network theory
type: Item
instance of: scholarly article
title: On global asymptotic stability of a class of nonlinear systems arising in neural network theory
zbMATH Open document ID: 0828.34039
author: Mauro Forti
published in: Journal of Differential Equations
publication date: 1996-01-02T00:00:00Z
review text: The author considers nonlinear dynamical systems of the form (1) \(\dot x= -{\mathcal D}(x)+ {\mathcal T}(x)h(x)\), where \(x= (x_1,\dots, x_n)\in \mathbb{R}^n\), \({\mathcal D}(x)= ({\mathcal D}_1(x_1),\dots, {\mathcal D}_n(x_n))\) and \(h(x)= (h_1(x_1),\dots, h_n(x_n))\) are vector fields of \(\mathbb{R}^n\) and \({\mathcal T}(x)\) is an \(n\times n\) matrix. \(\mathcal D\), \(h\) and \(\mathcal T\) are assumed to be as regular as required to guarantee existence, uniqueness and continuous dependence of solutions. Moreover, \({\mathcal D}(0)= h(0)= 0\). This class of systems includes for instance the so-called additive neural network model widely employed for real time signal processing. Using a Lyapunov approach, and under appropriate assumptions, the author proves a number of theorems on global asymptotic stability of (1), which turn out to be more general than previous results on the same subject. Finally, the author discusses applications to neural network models.
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 92B20
zbMATH DE Number: 665731
zbMATH Keywords: additive neural network model
zbMATH Keywords: Lyapunov approach
zbMATH Keywords: global asymptotic stability
reviewed by: Andrea Bacciotti
MaRDI profile type: Publication
full work available at URL: jdeq.1994.1123
OpenAlex ID: W2048646957
DOI: 10.1006/JDEQ.1994.1123
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description: scientific article; zbMATH DE number 665731