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

共 21 条

[11]

NUSSBAUM RD, 1974, ANN MAT PUR APPL, V10, P263

[12] Bifurcations, stability, and monotonicity properties of a delayed neural network model [J].

Olien, L ;

Belair, J .

PHYSICA D, 1997, 102 (3-4) :349-363

[13] A novel criterion for global asymptotic stability of BAM neural networks with tine delays [J].

Park, JH .

CHAOS SOLITONS & FRACTALS, 2006, 29 (02) :446-453

[14]

Park JH, 2006, CHAOS SOLITON FRACT, V30, P897, DOI 10.1016/j.chaos.2005.08.147

[15] Chaos control of Bonhoeffer-van der Pol oscillator using neural networks [J].

Ramesh, M ;

Narayanan, S .

CHAOS SOLITONS & FRACTALS, 2001, 12 (13) :2395-2405

[16] Periodic solutions of planar systems with two delays [J].

Ruan, SG ;

Wei, JJ .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1999, 129 :1017-1032

[17] Stability and bifurcation in a neural network model with two delays [J].

Wei, JJ ;

Ruan, SR .

PHYSICA D, 1999, 130 (3-4) :255-272

[18] Symmetric functional differential equations and neural networks with memory [J].

Wu, JH .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 350 (12) :4799-4838

[19] Exponential stability of neural networks with variable delays via LMI approach [J].

Yang, Haifeng ;

Chu, Tianguang ;

Zhang, Cishen .

CHAOS SOLITONS & FRACTALS, 2006, 30 (01) :133-139

[20] New stability conditions for neural networks with constant and variable delays [J].

Zhang, Q ;

Wei, XP ;

Xu, J .

CHAOS SOLITONS & FRACTALS, 2005, 26 (05) :1391-1398

← 1 2 3 →