Global asymptotic stability of high-order delay Hopfield neural networks with time-varying coefficients
type: Item
instance of: scholarly article
title: Global asymptotic stability of high-order delay Hopfield neural networks with time-varying coefficients
zbMATH Open document ID: 1106.34050
DOI: 10.4171/ZAA/1249
author: Peiguang Wang
author: Hairong Lian
author: Yonghong Wu
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2006-03-10T00:00:00Z
review text: Using the Brouwer fixed-point theorem and the method of Lyapunov functionals, the authors find conditions for existence and global asymptotic stability of the equilibrium of neural networks of the type \[ u_i'(t)= -a_i(t) u_i(t)+ b_i(t)+ \sum_j W_{ij}(t) g_j(u_j(t- \tau))+ \sum_{j,k} W_{ijk}(t) g_j(u_j(t-\tau)) g_k(u_k(t- \tau)), \] \(i= 1,2,\dots, n\). Here, \(a_i\), \(b_i\), \(g_i\), \(W_{ij}\) and \(W_{ijk}\) are continuous bounded functions and \(a_i(t)> 0\).
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 92B20
zbMATH DE Number: 5011364
zbMATH Keywords: neural networks
zbMATH Keywords: global asymptotic stability
zbMATH Keywords: Lyapunov functional
reviewed by: Mihail M. Konstantinov
MaRDI profile type: Publication
cites work: Stability analysis of delayed neural networks
cites work: High-order absolutely stable neural networks
cites work: On global asymptotic stability of a class of nonlinear systems arising in neural network theory
cites work: Stability in asymmetric Hopfield nets with transmission delays
cites work: Theory of functional differential equations. 2nd ed
cites work: On the global convergence of a class of functional differential equations with applications in neural network theory
full work available at URL: https://doi.org/10.4171/zaa/1249
OpenAlex ID: W1968916389
description: scientific article; zbMATH DE number 5011364