Stable periodic orbits in nonlinear discrete-time neural networks with delayed feedback
type: Item
instance of: scholarly article
title: Stable periodic orbits in nonlinear discrete-time neural networks with delayed feedback
zbMATH Open document ID: 1051.39016
DOI: 10.1016/S0898-1221(03)00066-X
author: Zhan Zhou
author: Jianhong Wu
publication date: 2004-08-06T00:00:00Z
review text: The authors consider a nonlinear discrete-time system \(x(n+1) = x(n)+g(y(n-k))\), \(y(n+1) = y(n)-g(x(n-k))\), \(n\in \mathbb{N}\) arising as a discrete-time network of two neurons with McCulloch-Pitts nonlinearity, where \(\beta\in (0,1), k\) is a positive integer, and \(g\) is a signal transmission function with a threshold \(\sigma\). The authors show that there exist a stable \(4(k+1)\)-periodic orbit in some regions of the parameters \((\beta,\sigma)\), and analyses asymptotic behavior of the system in other regions of \((\beta,\sigma).\)
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 92B20
Mathematics Subject Classification ID: 93C55
zbMATH DE Number: 2082204
zbMATH Keywords: discrete-time neural networks
zbMATH Keywords: delay
zbMATH Keywords: periodic orbits
zbMATH Keywords: stability
zbMATH Keywords: McCulloch-Pitts nonlinearity
zbMATH Keywords: asymptotic behavior
reviewed by: Jinde Cao
MaRDI profile type: Publication
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full work available at URL: s0898-1221(03)00066-x
OpenAlex ID: W2031377120
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 2082204