Bifurcation analysis in a recurrent neural network model with delays
type: Item
instance of: scholarly article
title: Bifurcation analysis in a recurrent neural network model with delays
zbMATH Open document ID: 1268.94044
author: Yuting Ding
author: Weihua Jiang
author: P. Yu
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2012-12-20T00:00:00Z
review text: The aim of this paper is to investigate the dynamical behavior of a three-node recurrent network model with four discrete time delays. After the introduction, the stability of the trivial equilibrium and the existence of several types of bifurcation are analyzed in Section 2. Using the method of multiple time scales (MTS), the authors derive in Section 3 the normal form of a nonlinear differential equation system associated with the Hopf-zero bifurcation, while Section 4 obtains the normal forms for non-resonant Hopf bifurcations. Section 5 studies the Hopf-zero bifurcation and double Hopf bifurcation, providing the corresponding critical points. Numerical simulations are presented for the verification of the analytical approach. In particular, for the resonant double Hopf bifurcation, numerical expressions for certain parameter values are found, although a closed-form solution of the non-trivial steady-state solutions is difficult to be obtained. The observed concordance between the analytical predictions and numerical simulations for the solutions of amplitude and frequency shows that the proposed method provides an efficient tool for the study of real problems.
Mathematics Subject Classification ID: 94C05
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 92B20
zbMATH DE Number: 6117612
zbMATH Keywords: three-node recurrent neural network
zbMATH Keywords: Hopf-zero bifurcation
zbMATH Keywords: double Hopf bifurcation
zbMATH Keywords: normal form
zbMATH Keywords: multiple time scales
zbMATH Keywords: steady-state solutions
MaRDI profile type: Publication
full work available at URL: j.cnsns.2012.07.002
OpenAlex ID: W2100513010
DOI: 10.1016/J.CNSNS.2012.07.002
description: scientific article; zbMATH DE number 6117612