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Applied Mathematics and Mechanics

, Volume 26, Issue 3, pp 327–335 | Cite as

Global dynamics of delayed bidirectional associative memory (BAM) neural networks

  • Zhou Jin
  • Liu Zeng-rong
  • Xiang Lan
Article

Abstract

Without assuming the smoothness, monotonicity and boundedness of the activation functions, some novel criteria on the existence and global exponential stability of equilibrium point for delayed bidirectional associative memory (BAM) neural networks are established by applying the Liapunov functional methods and matrix-algebraic techniques. It is shown that the new conditions presented in terms of a nonsingular M matrix described by the networks parameters, the connection matrix and the Lipschitz constant of the activation functions, are not only simple and practical, but also easier to check and less conservative than those imposed by similar results in recent literature.

Key words

bidirectional associative memory (BAM) neural network global exponential stability Liapunov function 

Chinese Library Classification

O175 TN911 

2000 Mathematics Subject Classification

34K20 34K35 92B20 

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References

  1. [1]
    Mohamad S. Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks[J].Physica D, 2001,159(3):233–251.MATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Liao X F, Yu J B, Chen G. Novel stability criteria for bidirectional associative memory neural networks with time delays [J].International Journal of Circuit Theory and Applications, 2002,30(3): 519–546.MATHCrossRefGoogle Scholar
  3. [3]
    Kosko B. Bidirectional associative memories[J].IEEE Transactions on Systems, Man, and Cybernetics, 1988,18(1):49–60.MathSciNetCrossRefGoogle Scholar
  4. [4]
    Kosko B. Unsupervised learning in noise[J].IEEE Transactions on Neural Networks, 1990,1(1): 44–57.CrossRefGoogle Scholar
  5. [5]
    Kosko B. Structural stability of unsupervised learning in feedback neural networks[J].IEEE Transactions on Automatic Control, 1991,36(5):785–790.MATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    Maundy B, Masry E. A switched capacitor bidirectional associative memory[J].IEEE Transactions on Circuits and Systems, 1990,37(12):1568–1572.CrossRefGoogle Scholar
  7. [7]
    Gopalsamy K, He X Z. Delay-independent stability in bidirectional associative memory networks [J].IEEE Transactions on Neural Networks, 1994,5(7):998–1002.CrossRefGoogle Scholar
  8. [8]
    Liao X F, Wong K W, Yu J B. Novel stability conditions for cellular neural networks with time delay[J].International Journal of Bifurcation and Chaos, 2001,11(12):1835–1864.Google Scholar
  9. [9]
    Morita M. Associative memory with non-monotone dynamics[J].Neural Networks, 1993,6(1): 115–126.CrossRefGoogle Scholar
  10. [10]
    Yoshizawa S, Morita M, Amari S. Capacity of associative memory using a non-monotonic neuron networks[J].Neural Networks, 1993,6(2):167–176.CrossRefGoogle Scholar
  11. [11]
    Kennedy M P, Chua L O. Neural networks for nonlinear programming[J].IEEE Transactions on Circuits and Systems, 1988,35(4):554–562.MathSciNetCrossRefGoogle Scholar
  12. [12]
    Zhou Jin, Liu Zengrong, Chen Guanrong. Dynamics of delayed periodic neural networks[J].Neural Networks, 2004,16(1):87–101.Google Scholar
  13. [13]
    Zhou Jin, Chen Tianping, Xiang Lan. Robust synchronization of coupled delayed recurrent neural networks[A].Advances in Neural Networks-ISNN, Lecture Notes in Computer Science[C]. Springer-Verlag, Berlin Heidelberg, New York, 2004,3173(1): 144–149.Google Scholar
  14. [14]
    Chen Guanrong, Zhou Jin, Liu Zengrong. Global synchronization of coupled delayed neural networks and applications to chaotic CNN models [J].International Journal of Bifurcation and Chaos, 2004,14(7):2229–2240.MathSciNetCrossRefGoogle Scholar
  15. [15]
    Xiang Lan, Zhou Jin, Liu Zengronget al. On the asymptotic behavior of Hopfield neural network with periodic inputs[J].Applied Mathematics and Mechanics (English Edition), 2002,23(12): 1367–1373.MathSciNetCrossRefGoogle Scholar
  16. [16]
    Hale J K.Introduction to Functional Differential Equations [M]. 2nd Edition. Springer-Verlag, Berlin Heidelberg, New York, 1977.Google Scholar

Copyright information

© Editorial Committee of Appl. Math. Mech. 2005

Authors and Affiliations

  1. 1.Institute of Applied MathematicsHebei University of TechnologyTianjinP.R. China
  2. 2.Institute of MathematicsFudan UniversityShanghaiP. R. China
  3. 3.Department of MathematicsShanghai UniversityShanghaiP.R. China
  4. 4.Department of PhysicsHebei University of TechnologyTianjinP. R. China

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