Stability analysis of a single neuron model with delay

被引：12

作者：

Gyori, I ^{[1
]}

Hartung, F ^{[1
]}

机构：

[1] Univ Veszprem, Dept Math & Comp, H-8201 Veszprem, Hungary

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2003年 / 157卷 / 01期

基金：

匈牙利科学研究基金会;

关键词：

delayed cellular neural networks; global asymptotic stability; numerical approximations;

D O I：

10.1016/S0377-0427(03)00376-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the asymptotic behavior and numerical approximation of the single neuron model equation x(t)=-dx(t)+af(x(t))+bf(x(t-tau))+I, t greater than or equal to 0 (1), where d > 0 and f(x) = 0.5(\x+1\-\x-1\). We obtain new sufficient conditions for global asymptotic stability of constant equilibriums of (1), give several numerical examples to illustrate our results; and formulate conjectures on the asymptotic behavior of the solutions based on our numerical experiments. (C) 2003 Elsevier B.V. All rights reserved.

引用

页码：73 / 92

页数：20

共 29 条

[21]

Ratliff F., 1974, STUDIES EXCITATION I

[22] CELLULAR NEURAL NETWORKS WITH NONLINEAR AND DELAY-TYPE TEMPLATE ELEMENTS AND NONUNIFORM GRIDS [J].

ROSKA, T ;

CHUA, LO .

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, 1992, 20 (05) :469-481

[23] STABILITY AND DYNAMICS OF DELAY-TYPE GENERAL AND CELLULAR NEURAL NETWORKS [J].

ROSKA, T ;

WU, CW ;

BALSI, M ;

CHUA, LO .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 1992, 39 (06) :487-490

[24]

Smith H. L, 2008, Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems: an introduction to the theory of competitive and cooperative systems No

[25] A new sufficient condition for complete stability of cellular neural networks with delay [J].

Takahashi, N .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS, 2000, 47 (06) :793-799

[26] Global dynamics of Hopfield neural networks involving variable delays [J].

Xu, DY ;

Zhao, HY ;

Zhu, H .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2001, 42 (1-2) :39-45

[27] Global stability analysis in delayed Hopfield neural network models [J].

Zhang, JY ;

Jin, XS .

NEURAL NETWORKS, 2000, 13 (07) :745-753

[28]

Zubik-Kowal B, 1998, STUD SCI MATH HUNG, V34, P413

[29]

[No title captured]

← 1 2 3 →