Bifurcation of a three-unit neural network
type: Item
instance of: scholarly article
title: Bifurcation of a three-unit neural network
zbMATH Open document ID: 1215.34085
author: Yaonan Wang
author: Shaofen Zou
author: Lihong Huang
published in: Applied Mathematics and Computation
publication date: 2010-10-25T00:00:00Z
review text: The author considers a class of delay differential equations that models a time-delayed connected network of three neurons without self-feedback. The boundary of the stability region is estimated by discussing the change of the number of eigenvalues with zero real part. Then, the author investigates the existence of bifurcation phenomena of codimension one/two of the trivial equilibrium by considering the intersections of some parameter curves, which correspond to a zero root or pure imaginary roots. Some numerical simulations are given to demonstrate the rich dynamical behavior near the equivariant Pitchfork-Hopf bifurcation points, Hopf-Hopf bifurcation points and some higher codimension bifurcation points. The paper is very interesting and the ideas in this paper can be applied to the investigation of large ring networks.
reviewed by: Xiaodi Li
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92B20
Mathematics Subject Classification ID: 34K60
zbMATH DE Number: 5804950
zbMATH Keywords: neural network
zbMATH Keywords: delay differential equation
zbMATH Keywords: stability
zbMATH Keywords: bifurcation
zbMATH Keywords: equivariance
MaRDI profile type: Publication
full work available at URL: j.amc.2010.06.034
OpenAlex ID: W2012833679
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DOI: 10.1016/J.AMC.2010.06.034
description: scientific article; zbMATH DE number 5804950