GLOBAL HOPF BIFURCATION ANALYSIS OF A SIX-DIMENSIONAL FITZHUGH-NAGUMO NEURAL NETWORK WITH DELAY BY A SYNCHRONIZED SCHEME

被引：7

作者：

Han, Fang ^{[1
]}

Zhen, Bin ^{[2
]}

Du, Ying ^{[3
]}

Zheng, Yanhong ^{[4
]}

Wiercigroch, Marian ^{[5
]}

机构：

[1] Donghua Univ, Sch Informat Sci & Technol, Shanghai 201620, Peoples R China

[2] Wuhan Univ Technol, Sch Civil & Architecture Engn, Wuhan 430070, Peoples R China

[3] E China Univ Sci & Technol, Inst Cognit Neurodynam, Sch Sci, Shanghai 200237, Peoples R China

[4] Fujian Normal Univ, Sch Math & Comp Sci, Fuzhou 350007, Peoples R China

[5] Univ Aberdeen, Ctr Appl Dynam Res, Aberdeen AB24 3UE, Scotland

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2011年 / 16卷 / 02期

基金：

上海市自然科学基金; 中国国家自然科学基金;

关键词：

Global Hopf bifurcation; FitzHugh-Nagumo model; neural network; delay; synchronize; MODELS;

D O I：

10.3934/dcdsb.2011.16.457

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Global Hopf bifurcation analysis is carried out on a six-dimensional FitzHugh-Nagumo (FHN) neural network with a time delay. First, the existence of local Hopf bifurcations of the system is investigated and the explicit formulae which can determine the direction of the bifurcations and the stability of the periodic solutions are derived using the normal form method and the center manifold theory. Then the sufficient conditions for the system to have multiple periodic solutions when the delay is far away from the critical values of Hopf bifurcations are obtained by using the Wu's global Hopf bifurcation theory and the Bendixson's criterion. Especially, a synchronized scheme is used during the analysis to reduce the dimension of the system. Finally, example numerical simulations are given to support the theoretical analysis.

引用

页码：457 / 474

页数：18

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