Bogdanov-Takens singularity in a network of two coupled neurons with delayed feedbacks
type: Item
instance of: scholarly article
title: Bogdanov-Takens singularity in a network of two coupled neurons with delayed feedbacks
zbMATH Open document ID: 1191.34090
author: Cun-Hua Zhang
author: Xiang-Ping Yan
published in: Journal of Applied Mathematics and Computing
publication date: 2009-10-26T00:00:00Z
review text: A retarded functional differential equation with multiple discrete delays representing a network of two coupled neurons with delayed feedback is studied. By regarding the connection weights as the bifurcation parameters and analyzing the spectrum of the infinitesimal generator of the strongly continuous semigroup generated by the flows of the linearized system of the original system at the zero equilibrium, the phenomenon that the system under consideration can exhibit a Bogdanov-Takens bifurcation at the origin when the connection weights take a certain critical value. Based on the center manifold reduction and the normal form method for retarded functional differential equations, the second order normal form on the center manifold is obtained.
reviewed by: Qintao Gan
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K17
Mathematics Subject Classification ID: 34K19
zbMATH DE Number: 5620594
zbMATH Keywords: coupled neuron
zbMATH Keywords: delayed feedback
zbMATH Keywords: discrete delay
zbMATH Keywords: Bogdanov-Takens singularity
zbMATH Keywords: normal form
MaRDI profile type: Publication
full work available at URL: s12190-008-0150-4
OpenAlex ID: W2058780874
cites work: Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity
cites work: On a planar system modelling a neuron network with memory
cites work: Delay induced periodicity in a neural netlet of excitation and inhibition
cites work: Two-parameter bifurcations in a network of two neurons with multiple delays
cites work: Theory of functional differential equations. 2nd ed
cites work: Q3930015
cites work: Neurons with graded response have collective computational properties like those of two-state neurons.
cites work: HOPF BIFURCATION OF A TWO-NEURON NETWORK WITH DIFFERENT DISCRETE TIME DELAYS
cites work: Bifurcations, stability, and monotonicity properties of a delayed neural network model
cites work: Construction of third-order WNND scheme and its application in complex flow
cites work: Stability and bifurcation in a neural network model with two delays.
cites work: Bifurcation analysis and existence of periodic solutions in a simple neural network with delays
cites work: Homoclinic orbits and Hopf bifurcations in delay differential systems with T-B singularity
DOI: 10.1007/S12190-008-0150-4
description: scientific article; zbMATH DE number 5620594