Applied Mathematics and Mechanics

, Volume 23, Issue 12, pp 1367–1373 | Cite as

On the asymptotic behavior of hopfield neural network with periodic inputs

  • Xiang Lan
  • Zhou Jin
  • Liu Zeng-rong
  • Sun Shu


Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neural network with periodic inputs are given by using Mawhin's coincidence degree theory and Liapunov's function method.

Key words

Hopfield neural network periodic solution global exponential stability concidence degree Liapunov's function 

CLC numbers

O175 TN911 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Hopfield J J. Neural networks and physical system with emergent collective computational abilities [J].Proc Nat Academy Sci, 1982,79(4): 2554–2558.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Hopfield J J. Neurons with graded response have collective computational properties like those of two-state neurons[J].Proc Nat Academy Sci, 1984,81(5): 3088–3092.CrossRefGoogle Scholar
  3. [3]
    LIAO Xiao-xin. Stability of Hopfield networks[J].Science in China Ser A, 1993,23(10): 1025–1035. (in Chinese)Google Scholar
  4. [4]
    LIANG Xue-bin, WU Li-de. Global exponential stability of Hopfield networks and applications [J].Science in China Ser A, 1995,25(5): 523–532. (in Chinese)Google Scholar
  5. [5]
    Guan Z H, Chen G. On the equilibria, stability and instability of Hopfield neural networks [J].IEEE Trans Neural Networks, 2000,11(2): 534–539.MathSciNetCrossRefGoogle Scholar
  6. [6]
    LI Tie-cheng, WANG Duo. On the asymptotic behavior of a class artificial neural network with periodic input[J].JCU-Appl Math Ser A, 1997,12(1): 25–28. (in Chinese)Google Scholar
  7. [7]
    HUANG Xian-kai. On the existence and stability of periodic solutions for Hopfield neural network equation with delay[J],Applied Mathematics and Mechnics (English Edition), 1999,20(10): 1116–1120.Google Scholar
  8. [8]
    Gao J. Periodic oscillation and exponential stability of delayed CNN[J].Physics Letters A, 2000,270(3/4): 157–163.Google Scholar
  9. [9]
    Gain R E, Mawhin J L.Coincidence Degree and Nonlinear Differential Equations [M].Lecture Note in Math,567, Berlin: Springer-Verlag, 1977, 40–41.Google Scholar
  10. [10]
    Yoshizawa T.Stability Theory by Liapunov's Second Method[M]. Tokyo: The Math Soc of Japan, 1996, 165–169.Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics All rights reserved 1980

Authors and Affiliations

  • Xiang Lan
    • 1
  • Zhou Jin
    • 1
    • 2
  • Liu Zeng-rong
    • 2
  • Sun Shu
    • 3
  1. 1.Department of PhysicsHebei University of TechnologyTianjinP R China
  2. 2.Department of MathematicsShanghai UniversityShanghaiP R China
  3. 3.Naval Submarine AcademyQingdaoP R China

Personalised recommendations