Bogdanov-Takens bifurcation in a single inertial neuron model with delay

被引：96

作者：

He, Xing ^{[1
]}

Li, Chuandong ^{[1
]}

Shu, Yonglu ^{[2
]}

机构：

[1] Chongqing Univ, Coll Comp Sci, Chongqing 400030, Peoples R China

[2] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

来源：

NEUROCOMPUTING | 2012年 / 89卷

基金：

中国国家自然科学基金;

关键词：

Bogdanov-Takens bifurcation; Inertial neuron model; Homoclinic bifurcation; Heteroclinic bifurcation; FUNCTIONAL-DIFFERENTIAL EQUATIONS; NORMAL FORMS; STABILITY; DYNAMICS; SYSTEMS; CHAOS;

D O I：

10.1016/j.neucom.2012.02.019

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

In this paper, we study a retarded functional differential equation modeling a single neuron with inertial term subject to time delay. Bogdanov-Takens bifurcation is investigated by using center manifold reduction and the normal form method for RFDE. We get the versal unfolding of the norm forms at the B-T singularity and show that the model can exhibit saddle-node bifurcation, pitchfork bifurcation, homoclinic bifurcation, heteroclinic bifurcation and double limit cycle bifurcation. Some numerical simulations are given to support the analytic results. (c) 2012 Elsevier B.V. All rights reserved.

引用

页码：193 / 201

页数：9

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