Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with Delays

A class of discrete-time Cohen-Grossberg neural networks with delays is investigated in this paper. By analyzing the corresponding characteristic equations, the asymptotical stability of the null solution and the existence of Neimark-Sacker bifurcations are discussed. By applying the normal form the...

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Main Authors: Qiming Liu, Rui Xu, Zhiping Wang
Format: Article
Language:English
Published: Wiley 2011-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2011/403873
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author Qiming Liu
Rui Xu
Zhiping Wang
author_facet Qiming Liu
Rui Xu
Zhiping Wang
author_sort Qiming Liu
collection DOAJ
description A class of discrete-time Cohen-Grossberg neural networks with delays is investigated in this paper. By analyzing the corresponding characteristic equations, the asymptotical stability of the null solution and the existence of Neimark-Sacker bifurcations are discussed. By applying the normal form theory and the center manifold theorem, the direction of the Neimark-Sacker bifurcation and the stability of bifurcating periodic solutions are obtained. Numerical simulations are given to illustrate the obtained results.
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spelling doaj-art-682cd497494742e8bb589a0f1b24f8d12025-08-20T02:06:41ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2011-01-01201110.1155/2011/403873403873Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with DelaysQiming Liu0Rui Xu1Zhiping Wang2Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaInstitute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaInstitute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaA class of discrete-time Cohen-Grossberg neural networks with delays is investigated in this paper. By analyzing the corresponding characteristic equations, the asymptotical stability of the null solution and the existence of Neimark-Sacker bifurcations are discussed. By applying the normal form theory and the center manifold theorem, the direction of the Neimark-Sacker bifurcation and the stability of bifurcating periodic solutions are obtained. Numerical simulations are given to illustrate the obtained results.http://dx.doi.org/10.1155/2011/403873
spellingShingle Qiming Liu
Rui Xu
Zhiping Wang
Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with Delays
Discrete Dynamics in Nature and Society
title Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with Delays
title_full Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with Delays
title_fullStr Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with Delays
title_full_unstemmed Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with Delays
title_short Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with Delays
title_sort stability and bifurcation of a class of discrete time cohen grossberg neural networks with delays
url http://dx.doi.org/10.1155/2011/403873
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AT zhipingwang stabilityandbifurcationofaclassofdiscretetimecohengrossbergneuralnetworkswithdelays