Global Dynamics of Delayed Bidirectional Associative Memory (BAM) Neural Networks

ZHOU Jin; LIU Zeng-rong; XIANG Lan

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(3): 300-308

ZHOU Jin, LIU Zeng-rong, XIANG Lan. Global Dynamics of Delayed Bidirectional Associative Memory (BAM) Neural Networks[J]. Applied Mathematics and Mechanics, 2005, 26(3): 300-308.

Citation:

ZHOU Jin, LIU Zeng-rong, XIANG Lan. Global Dynamics of Delayed Bidirectional Associative Memory (BAM) Neural Networks[J]. Applied Mathematics and Mechanics, 2005, 26(3): 300-308.

Citation:

ZHOU Jin, LIU Zeng-rong, XIANG Lan. Global Dynamics of Delayed Bidirectional Associative Memory (BAM) Neural Networks[J]. Applied Mathematics and Mechanics, 2005, 26(3): 300-308.

PDF( 368 KB)

Global Dynamics of Delayed Bidirectional Associative Memory (BAM) Neural Networks

1.
Institute of Applied Mathematics, Hebei University of Technology, Tianjin 300130, P. R. China;

Received Date: 2003-07-04
Rev Recd Date: 2004-11-30
Publish Date: 2005-03-15

Abstract

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

FullText(HTML)

References(16)

References

[1]	Mohamad S.Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks[J]Physica D,2001,159(3):233—251.
[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. doi: 10.1002/cta.206
[3]	Kosko B. Bidirectional associative memories[J]. IEEE Transactions on Systems,Man,and Cybernetics,1988,18(1):49—60. doi: 10.1109/21.87054
[4]	Kosko B. Unsupervised learning in noise[J].IEEE Transactions on Neural Networks,1990,1(1):44—57. doi: 10.1109/72.80204
[5]	Kosko B. Structural stability of unsupervised learning in feedback neural networks[J].IEEE Transactions on Automatic Control,1991,36(5):785—790. doi: 10.1109/9.85058
[6]	Maundy B,Masry E. A switched capacitor bidirectional associative memory[J].IEEE Transactions on Circuits and Systems,1990,37(12):1568—1572. doi: 10.1109/31.101281
[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. doi: 10.1109/72.329700
[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. doi: 10.1142/S0218127401003097
[9]	Morita M. Associative memory with non-monotone dynamics [J].Neural Networks,1993,6(1):115—126. doi: 10.1016/S0893-6080(05)80076-0
[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. doi: 10.1016/0893-6080(93)90014-N
[11]	Kennedy M P,Chua L O. Neural networks for nonlinear programming[J].IEEE Transactions on Circuits and Systems,1988,35(4):554—562. doi: 10.1109/31.1783
[12]	ZHOU Jin,LIU Zeng-rong,CHEN Guan-rong. Dynamics of delayed periodic neural networks[J].Neural Networks,2004,16(1):87—101.
[13]	ZHOU Jin,CHEN Tian-ping,XIANG Lan. Robust synchronization of coupled delayed recurrent neural networks,Advances in Neural Networks-ISNN[A].Lecture Notes in Computer Science[C].Berlin Heidelberg,New York:Springer-Verlag,2004,3173(1):144—149.
[14]	CHEN Guan-rong,ZHOU Jin,LIU Zeng-rong. 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. doi: 10.1142/S0218127404010655
[15]	向兰，周进，刘曾荣，等.具有周期输入Hopfield型神经网络的全局渐近性质[J].应用数学和力学，2002,23(12):1220—1226.
[16]	Hale J K.Introduction to Functional Differential Equations [M].2nd Edition.New York:Berlin Heidelberg:Springer-Verlag,1977.