Global existence of periodic solutions in a tri-neuron network model with delays

被引：93

作者：

Wei, JJ

Li, MY ^{[1
]}

机构：

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

[2] Harbin Inst Technol, Dept Math, Harbin 150001, Heilongjiang, Peoples R China

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2004年 / 198卷 / 1-2期

基金：

加拿大自然科学与工程研究理事会; 美国国家科学基金会; 中国国家自然科学基金;

关键词：

neural networks; delay systems; Hopf bifurcations; periodic solutions;

D O I：

10.1016/j.physd.2004.08.023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a delayed differential system that models a network of three neurons with memory. Using a global Hopf bifurcation theorem for FDE due to J. Wu and a Bendixson's criterion for high-dimensional ODE due to Li and Muldowney, we obtain a group of sufficient conditions for the system to have multiple periodic solutions when the sum of delays is sufficiently large. (C) 2004 Elsevier B.V. All rights reserved.

引用

页码：106 / 119

页数：14

共 21 条

[1]

[Anonymous], 1994, J DIFFERENTIAL EQUAT, DOI DOI 10.1006/JDEQ.1993.1097

[2]

BALDI P, 1994, IEEE T NEURAL NETWOR, V5, P610

[3] Negative criteria for the existence of periodic solutions in a class of delay-differential equations [J].