Global existence of periodic solutions in a special neural network model with two delays

被引：5

作者：

Dong, Ying ^{[1
]}

Sun, Chengjun ^{[2
]}

机构：

[1] Shandong Univ, Dept Math, Weihai 264209, Peoples R China

[2] McGill Univ, Dept Biol, Montreal, PQ H3A 1B1, Canada

来源：

CHAOS SOLITONS & FRACTALS | 2009年 / 39卷 / 05期

基金：

加拿大自然科学与工程研究理事会;

关键词：

FUNCTIONAL-DIFFERENTIAL EQUATIONS; VARIABLE DELAYS; TIME-DELAY; STABILITY; BIFURCATION; CRITERION; DISCRETE; MEMORY; SYSTEM; CHAOS;

D O I：

10.1016/j.chaos.2007.06.106

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A simple neural network model with two delays is considered. By analyzing the associated characteristic transcendental equation, it is found that Hopf bifurcation occurs when file sum of two delays passes through a sequence of critical values. Using a global Hopf bifurcation theorem for FDE due to Wu [Wu J. Symmetric functional differential equations and neural networks with memory. Trans Amer Math Soc 1998;350:4799-838], a group of sufficient conditions for this model to have multiple periodic solutions are obtained when the sum of delay's is sufficiently large. Numerical simulations are presented to support the obtained theoretical results. (c) 2007 Elsevier Ltd. All rights reserved.

引用

页码：2249 / 2257

页数：9

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