Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays

Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays

A Cohen-Grossberg neural network with discrete delays is investigated in this paper. Sufficient conditions for the existence of local Hopf bifurcation are obtained by analyzing the distribution of roots of characteristic equation. Moreover, the direction and stability of Hopf bifurcation are obtaine...

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Main Authors: Qiming Liu, Sumin Yang
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/468584
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spelling doaj-08e0a4967e2e4232b53e3eaadd2999d32020-11-24T23:16:59ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/468584468584Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time DelaysQiming Liu0Sumin Yang1Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaDepartment of Information Engineering, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaA Cohen-Grossberg neural network with discrete delays is investigated in this paper. Sufficient conditions for the existence of local Hopf bifurcation are obtained by analyzing the distribution of roots of characteristic equation. Moreover, the direction and stability of Hopf bifurcation are obtained by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the obtained results.http://dx.doi.org/10.1155/2014/468584
collection DOAJ
language English
format Article
sources DOAJ
author Qiming Liu
Sumin Yang
spellingShingle Qiming Liu
Sumin Yang
Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays
Journal of Applied Mathematics
author_facet Qiming Liu
Sumin Yang
author_sort Qiming Liu
title Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays
title_short Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays
title_full Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays
title_fullStr Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays
title_full_unstemmed Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays
title_sort stability and hopf bifurcation of an n-neuron cohen-grossberg neural network with time delays
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2014-01-01
description A Cohen-Grossberg neural network with discrete delays is investigated in this paper. Sufficient conditions for the existence of local Hopf bifurcation are obtained by analyzing the distribution of roots of characteristic equation. Moreover, the direction and stability of Hopf bifurcation are obtained by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the obtained results.
url http://dx.doi.org/10.1155/2014/468584
work_keys_str_mv AT qimingliu stabilityandhopfbifurcationofannneuroncohengrossbergneuralnetworkwithtimedelays
AT suminyang stabilityandhopfbifurcationofannneuroncohengrossbergneuralnetworkwithtimedelays
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