• ISSN 0258-2724
  • CN 51-1277/U
  • EI Compendex
  • Scopus
  • Indexed by Core Journals of China, Chinese S&T Journal Citation Reports
  • Chinese S&T Journal Citation Reports
  • Chinese Science Citation Database
Volume 21 Issue 3
Jun.  2008
Turn off MathJax
Article Contents
LONG Lan, XU Xiaohui, ZHANG Jiye. Global Stability Analysis of Cohen-Grossberg Neural Networks with Unbounded Time Delays[J]. Journal of Southwest Jiaotong University, 2008, 21(3): 381-386.
Citation: LONG Lan, XU Xiaohui, ZHANG Jiye. Global Stability Analysis of Cohen-Grossberg Neural Networks with Unbounded Time Delays[J]. Journal of Southwest Jiaotong University, 2008, 21(3): 381-386.

Global Stability Analysis of Cohen-Grossberg Neural Networks with Unbounded Time Delays

  • Received Date: 23 Jul 2007
  • Publish Date: 25 Jun 2008
  • In order to apply the neural networks to optimization problems,the conditions ensuring the existence,uniqueness and global asymptotical stability of the equilibrium point of Cohen-Grossberg neural networks(CGNN)with unbounded time delays were investigated.Without assuming the boundedness,monotone and differentiability of the activation functions,the existence condition of the equilibrium point of CGNN was obtained.Using the vector Liapunov function method,the intero-differential inequalities with unbounded time delays were constructed,and the stability of the intero-differential inequalities were analyzed to obtain the criteria for the global asymptotical stability of the equilibrium point.Based on the criteria,the global asymptotic stability of CGNN can be get by judging whether the matrix constructed by the weighed coefficients,self-feedback functions and activation functions of CGNN is an M-matrix.Finally,an example was given to testify the validity of the criteria.

     

  • loading
  • COHEN M A,GROSSBERG S.Absolute stability and global pattern formation and parallel memory storage by competitive neural networks[J].IEEE Transactions on Systems,Man and Cybernetics Society,1983,13(5):815-825.[2] FORTI M,TESI A.New conditions for global stability of neural networks with application to linear and quadratic programming problems[J].IEEE Transactions on Circuits and Systems-I,1995,42(7):354-366.[3] ARIK S,TAVANOGLU V.On the global asymptotic stability of delayed cellular neural networks[J].IEEE Transactions on Circuits and Systems-I,2000,47(4):571-574.[4] GOPALSAMY K,HE X.Stability in asymmetric Hopfield nets with transmission delays[J].Physica D,1994,76(4):344-358.[5] SREE H R V,PHANEENDRA B R M.Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead zones[J].Neural Networks,1999,12(3)455-465.[6] ZHANG Jiye,SUDA Y,IWASA T.Absolutely exponential stability of a class of neural networks with unbounded delay[J].Neural Networks,2004,17(3):391-397.[7] ZHANG Jiye.Globally exponential stability of neural networks with variable delays[J].IEEE Transactions on Circuits and Systems-I,2003,50(2):288-291.[8] ZHANG Jiye,SUDA Y,KOMINE H.Global exponential stability of cohen-grossberg neural networks with variable delays[J].Physics Letter A,2005,338(1):44-50.[9] ZHANG Jiye.Global stability analysis in cellular neural networks with unbounded time delays[J].Applied Mathematics and Mechanics-English Edition,2004,25 (6):686-693.[10] 舒仲周,张继业,曹登庆.运动稳定性[M].北京:中国铁道出版社,2001:148-167.[11] 张克跃,任殿波,张继业.分布时滞动态神经网络的全局指数稳定性[J].西南交通大学学报,2008,43(1):57-61.ZHANG Keyue,REN Dianbo,ZHANG Jiye.Global exponential stability of dynamic neural networks with distributed delays[J].Journal of Southwest Jiaotong University,2008,43(1):57-61.[12] SILJIAK D D.Large-scale dynamic systems-stability and structure[M].New York:Elsevier North-Holland Inc.,1978:165-171.[13] 张继业,杨翊仁,曾京.无限维关联系统的弦稳定性[J].应用数学和力学,2000,21(7):715-720. ZHANG Jiye,YANG Yiren,ZENG Jing.String stability of infinite interconnected system[J].Applied Mathematics and Mechanics,2000,21(7):715-720.[14] HALE J K,LUNEL S M V.Introduction to functional differential equations[M].New York:Springer-Verlag,1993:130-150.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索
    Article views(2009) PDF downloads(459) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return