Hopf bifurcation in bidirectional associative memory neural networks with delays: Analysis and computation
type: Item
instance of: scholarly article
title: Hopf bifurcation in bidirectional associative memory neural networks with delays: Analysis and computation
zbMATH Open document ID: 1054.65076
author: Lin Wang
author: Xingfu Zou
published in: Journal of Computational and Applied Mathematics
publication date: 2004-08-16T00:00:00Z
review text: This paper is concerned with the stability behaviour of some delay differential equations that model bidirectional associative memory neural networks. The system under consideration has the form \(x_i'(t)=-x_i(t)+\sum_{j=1}^na_{ij}f_j(y_j(t-\tau_1))\), \(y_i'(t)=-y_i(t)+\sum_{j=1}^nb_{ij}g_j(y_j(t-\tau_2))\), \(i=1,\dots,N\), where \(a_{ij},b_{ij}\) are the constant connection weights through the neurons in two layers, \(f_i\) and \(g_i\) given activation functions and \(\tau_1,\tau_2\) constant delays. In this problem several sets of sufficient conditions on the data problem \(a_{ij},b_{ij},f_i,g_i\) that imply the asymptotic stability of the zero solution are given. Also the existence of Hopf bifurcations in terms of \(\tau=\tau_1+\tau_2\) is studied proving that for some \(\tau=\tau^*\) the above system has a branch of periodic solutions bifurcating from the zero solution near \(\tau=\tau^*\). Finally, a particular system with \(N=2\) neurons is considered to test the above theoretical results using the delay differential equations solver of \textit{L. F. Shampine} and \textit{S. Thompson} [Appl. Numer. Math. 37, 441--458 (2001; Zbl 0983.65079)].
Mathematics Subject Classification ID: 65L07
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 92B20
Mathematics Subject Classification ID: 34K25
zbMATH DE Number: 2091371
zbMATH Keywords: delay differential equations
zbMATH Keywords: bidirectional neural networks
zbMATH Keywords: stability
zbMATH Keywords: periodic solutions
zbMATH Keywords: Hopf bifurcation
reviewed by: Manuel Calvo
describes a project that uses: dde23
MaRDI profile type: Publication
full work available at URL: j.cam.2003.09.047
OpenAlex ID: W2137133243
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DOI: 10.1016/J.CAM.2003.09.047
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description: scientific article; zbMATH DE number 2091371