Dynamics of a class of nonlinear discrete-time neural networks
type: Item
instance of: scholarly article
title: Dynamics of a class of nonlinear discrete-time neural networks
zbMATH Open document ID: 1072.39018
author: Huiyan Zhu
author: Lihong Huang
publication date: 2005-03-08T00:00:00Z
review text: A second-order ordinary differential equation (ODE)-system with piecewise constant terms is transformed into a discrete nonlinear recurrence (\(\mathbb{R}^2\)-point map). Its properties are studied numerically, leading to ``interesting results'', which have turned out to be more complicated than expected. -- The unawoved reason for this cautious statement can be attributed to Birkhoff's proof that the space of functions defined by recurrences is larger than that defined by ODE-s, which extends Poincaré's proof that most ODE systems are non-integrable: In contemporary terminology this means that the corresponding dynamics are complex (`chaotic', although deterministic). Although the ODE-recurrence transformation is singular, the `observed' synchronized periodic solutions correspond to stable cycles. No unstable cycles are reported, although they are well-known to exist in nonlinear recurrences, their accumulations leading to homoclinic and heteroclinic points.
reviewed by: Igor Gumowski
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 92B20
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 37C29
zbMATH DE Number: 2142447
zbMATH Keywords: simulated neuron dynamics
zbMATH Keywords: exploratory analysis
zbMATH Keywords: discrete nonlinear description
zbMATH Keywords: artificial neural network
zbMATH Keywords: delay
zbMATH Keywords: convergence
zbMATH Keywords: periodicity
zbMATH Keywords: discrete nonlinear recurrence
zbMATH Keywords: stable cycles
zbMATH Keywords: homoclinic and heteroclinic points
MaRDI profile type: Publication
full work available at URL: j.camwa.2004.01.006
OpenAlex ID: W2024294559
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DOI: 10.1016/J.CAMWA.2004.01.006
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2142447