Bifurcation analysis in a recurrent neural network model with delays

被引：18
作者：
Ding, Yuting [1 ,2 ]
Jiang, Weihua [2 ]
Yu, Pei [1 ]
机构：
[1] Univ Western Ontario, Dept Appl Math, London, ON N6A 5B7, Canada
[2] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
来源：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2013年 / 18卷 / 02期
基金：
中国国家自然科学基金; 加拿大自然科学与工程研究理事会;
关键词：
Recurrent neural network model; Hopf-zero bifurcation; Double Hopf bifurcation; Normal form; Multiple time scales; HOPF-BIFURCATION; MULTIPLE SCALES; DIFFERENTIAL EQUATIONS; STABILITY ANALYSIS; GLOBAL STABILITY; FREQUENCY-DOMAIN; TIME DELAYS; OSCILLATIONS; EXISTENCE; PREDICTION;
D O I：
10.1016/j.cnsns.2012.07.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the dynamical behaviors of a three-node recurrent neural network model with four discrete time delays. We study several types of bifurcation, and use the method of multiple time scales to derive the normal forms associated with Hopf-zero bifurcation, non-resonant and resonant double Hopf bifurcations. Moreover, bifurcations are classified in two-dimensional parameter space near these critical points, and numerical simulations are presented to demonstrate the applicability of the theoretical results. (c) 2012 Elsevier B.V. All rights reserved.
引用
收藏
页码：351 / 372
页数：22
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