Stability and Hopf bifurcation in a three-neuron unidirectional ring with distributed delays
type: Item
instance of: scholarly article
title: Stability and Hopf bifurcation in a three-neuron unidirectional ring with distributed delays
zbMATH Open document ID: 1276.92008
author: Yanyan Han
author: Yongli Song
published in: Nonlinear Dynamics
publication date: 2013-01-04T00:00:00Z
review text: The authors study a unidirectional ring of three scalar cells which are coupled by a distributed delay: \[ x_{j+1}(t) = -x_{j+1}(t) + c_j\tanh \left[ \int_{-\infty}^{t}\kappa(t-s)x_j(s)ds\right],\;j=1,2,3, \] where the delay kernel is given by \(\kappa(s) = \beta e^{-\beta s}\). They give sufficient conditions for the stability of equilibria and determine critical parameter values for Hopf bifurcations. They use the method of multiple scales to determine direction and stability of the Hopf bifurcations and show that there exists a global Hopf bifurcation.
reviewed by: Leonhard Lücken
Mathematics Subject Classification ID: 92B20
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 6122177
zbMATH Keywords: neural networks
MaRDI profile type: Publication
full work available at URL: s11071-011-0269-y
OpenAlex ID: W2058524558
Wikidata QID: Q114954983
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DOI: 10.1007/S11071-011-0269-Y
description: scientific article; zbMATH DE number 6122177