[1]徐昌进,姚凌云.具有时滞的神经网络模型的分支分析[J].华侨大学学报(自然科学版),2012,33(6):694-698.[doi:10.11830/ISSN.1000-5013.2012.06.0694]
 XU Chang-jin,YAO Ling-yun.Bifurcation Analysis of a Delayed Neural Networks[J].Journal of Huaqiao University(Natural Science),2012,33(6):694-698.[doi:10.11830/ISSN.1000-5013.2012.06.0694]
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具有时滞的神经网络模型的分支分析()
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《华侨大学学报(自然科学版)》[ISSN:1000-5013/CN:35-1079/N]

卷:
第33卷
期数:
2012年第6期
页码:
694-698
栏目:
出版日期:
2012-11-20

文章信息/Info

Title:
Bifurcation Analysis of a Delayed Neural Networks
文章编号:
1000-5013(2012)06-0694-05
作者:
徐昌进 姚凌云
1.贵州财经大学 贵州省经济系统仿真重点实验室, 贵州 贵阳 550004;2. 贵州财经大学 图书馆, 贵州 贵阳 550004
Author(s):
XU Chang-jin YAO Ling-yun
1. Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550004, China; 2. Library, Guizhou University of Finance and Economics, Guiyang 550004, China
关键词:
神经网络 稳定性 Hopf分支 时滞
Keywords:
neural networks stability Hopf bifurcation delay
分类号:
O175.12
DOI:
10.11830/ISSN.1000-5013.2012.06.0694
文献标志码:
A
摘要:
研究一类具有时滞的神经网络模型.通过分析系统的特征方程及考虑不同的时滞对系统动力学行为的影响,得到系统的平衡点稳定及Hopf分支产生的条件.数值模拟验证了所得理论分析的结果的正确性,补充了前人的研究成果.
Abstract:
In this paper, a delayed neural networks model is investigated. By analyzing the associated characteristic equation and studying how the different delays affect the dynamical behavior of system, the condition of stability of equilibrium and the existence of Hopf bifurcation are obtained. Numerical simulations are carried out to justify the theoretical findings. Our result is a good complement to the earlier publications.

参考文献/References:

[1] HOPFIELD J.Neurons with graded response have collective computional properties like those of two-state neurons[J]. Proceedings of the National Academy of Sciences USA,1984,81(10):3088-3092.
[2] XU Chang-jin,TANG Xianhua,LIAO Mao-xin.Frequency domain analysis for bifurcation in a simplified tri-neuron BAM network model with two delays[J].Neural Networks,2010,23(7):872-880.
[3] XU Chang-jin,HE Xiao-fei,LI Pei-luan.Global existence of periodic solutions in a six-neuron BAM neural network model with discrete delays[J].Neurocomputing,2011,74(17):3257-3267.
[4] XU Chang-jin,TANG Xianhua,LIAO Mao-xin.Stability and bifurcation analysis of a six-neuron BAM neural network model with discrete delays[J].Neurocomputing,2011,74(5):689-707.
[5] ZHANG Zheng-qiu,YANG Yan,HUANG Ye-sheng.Global exponential stability of interval general BAM neural networks with reaction-diffusion terms and multiple time-varying delays[J].Neural Networks,2011,24(5):457-465.
[6] GUO Shang-jiang,YUAN Yuan.Delay-induced primary rhythmic behavior in a two-layer neural network[J].Neural Networks,2011,24(1):65-74.
[7] GUO Shang-jiang.Equivariant Hopf bifurcation for functional differential equations of mixed type[J].Applied Mathematics Letters,2011,24(5):724-730.
[8] 刘云辉,李钟慎.改进型模糊神经网络模型的构造[J].华侨大学学报:自然科学版,2010,31(3):256-259.
[9] HUANG Chuang-xia,HE Yi-gang,HUANG Li-hong,et al.Hopf bifurcation analysis of two neurons with three delays[J].Nonlinear Analysis: Real World Applications,2007,8(3):903-921.
[10] YUAN Shao-liang,LI Xue-mei.Stability and bifurcation analysis of an annular delayed neural network with self-connection [J].Neurocomputing,2010,73(16/17/18):2905-2912.
[11] OLIEN L,BELAIR J.Bifurcations,stability,and monotonicity properties of a delayed neural networks model[J].Physica D,1997,102(3/4):349-363.
[12] RUAN Shi-gui,WEI Jun-jie.On the zero of some transcendential functions with applications to stability of delay differential equations with two delays[J].Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis,2003,10(1):863-874.
[13] HALE J K,VERDUYN-LUNEL S M.Introduction to functional differential equations[M].New York:Springer-Verlag,1993.

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备注/Memo

备注/Memo:
收稿日期: 2012-03-01
通信作者: 徐昌进(1970-),男,副教授,主要从事泛函微分方程理论及其应用的研究.E-mail:mail:xcj403@126.com.
基金项目: 国家自然科学基金资助项目(60902044); 贵州省软科学基金资助项目(黔科合R字[2011]LKC2030); 贵州省科学技术基金资助项目(黔科合J字[2012]2011); 贵州财经大学博士科研启动项目(2010年度)
更新日期/Last Update: 2012-11-20