Existence and Stability Analysis of Discrete-time Fuzzy BAM Neural Networks with Delays and Impulses

In this paper, the discrete-time fuzzy BAM neural network with delays and impulses is studied. Sufficient conditions are obtained for the existence and global stability of a unique equilibrium of this class of fuzzy BAM neural networks with Lipschitzian activation functions without assuming their boundedness, monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time. Some numerical examples are given to demonstrate the effectiveness of the obtained results.

• Chao Wang
• Yongkun Li

• Discrete-time fuzzy BAM neural networks
• ımpulses
• global exponential stability
• global asymptotical stability
• equilibrium point.

[1] B. Kosko, Neural Networks and Fuzzy systems-A Dynamic System
Approach Machine Intelligence, Prentice-Hall, Englewood Cliffs, NJ,
1992.
[2] B. Kosko, Bi-directional associative memories, IEEE Trans. Syst. Man
Cybern. 18 (1988) 49-60.
[3] B. Kosko, Adaptive bidirectional associative memories, Appl. Opt. 26
(1987) 4947-4960.
[4] T. Kohonen, Self-organization and associative memory, New York,
Springer, 1988.
[5] J. Cao, Periodic oscillatory solution of bidirectional associative memory
networks with delays, Phys. Rev. E 61 (2000) 1825-1828.
[6] Y.K. Li, Existence and stability of periodic solutions for Cohen-Grossberg
neural networks with multiple delays, Chaos, Slitons and Fractals 20
(2004) 459-466.
[7] Y.K. Li, L.H. Lu, Global exponential stability and existence of periodic
solution of Hopfield-type neural networks with impulses, Phys. Lett. A
333 (2004) 62-71.
[8] Y. Xia, J. Cao, M. Lin, New results on the existence and uniqueness of
almost periodic solutions for BAM neural networks with continuously
distributed delays. Chaos, Solitons and Fractals 314 (2007) 928-36.
[9] Z. Guan, G. Chen, On delayed impulsive Hopfield neural networks,
Neural Networks 12 (1999) 273-280.
[10] H. Akca, R. Alassar, V. Covachev, Z. Covacheva, E. Al-Zahrani,
Continuous-time additive Hopfield-type neural networks with impulses,
J. Math. Anal. Appl. 290 (2004) 436-451.
[11] K. Gopalsamy, Stability of artificial neural networks with impulses,
Appl. Math. Comput. 154 (2004) 783-813.
[12] Z. Chen, J. Ruan, Global stability analysis of impulsive Cohen-
Grossberg neural networks with delays, Phys. Lett. A 345 (2005) 101-111.
[13] Y. Zhang, J.T. Sun, Stability of impulsive neural networks with time
delays, Phys. Lett. A 348 (2005) 44-50.
[14] D.Y. Xu, Z.C. Yang, Impulsive delay differential inequality and stability
of neural networks, J. Math. Anal. Appl. 305 (2005) 107-120.
[15] Z.C. Yang, D.Y. Xu, Impulsive effects on stability of Cohen-Grossberg
neural networks with variable delays, Appl. Math. Comput. 177 (2006)
63-78.
[16] W. Zhu, D.Y. Xu, Z.C. Yang, Global exponential stability of impulsive
delay difference equation, Appl. Math. Comput. 181 (2006) 65-72.
[17] X. Huang, J. Cao, D.S. Huang, LMI-based approach for delay-dependent
exponential stability analysis of BAM neural networks, Chaos, Soliton
and Fractals 24 (2005) 885-898.
[18] X. Liao, Y. Liao, Y. Liao, Stability of bi-directional associative memory
neural networks with delays, J. Electron. 15 (1998) 372-377.
[19] Ju H. Park, Robust stability of bidirectional associative memory neural
networks with time delays, Phys. Lett. A 349 (2006) 494-499.
[20] Y.K. Li, Global exponential stability of BAM neural networks with
delays and impulses, Chaos, Soliton and Fractals 24 (2005) 279-285.
[21] X.Y. Lou, B.T. Cui, Global asymptotic stability of delay BAM neural
networks with impulses, Chaos, Soliton and Fractals 29 (2006) 1023-
1031.
[22] X.Y. Lou, B.T. Cui, Global asymptotic stability of delay BAM neural
networks with impulses based on matrix theory, Appl. Math. Modelling
32 (2008) 232-239.
[23] T. Yang, L. Yang, The global stability of fuzzy cellular neural networks,
IEEE Trans. Cric. Syst. I 43 (10) (1996) 880-883.
[24] T. Yang, L. Yang, C.W. Wu, L.O. Chua, Fuzzy cellular neural networks:
theory, in: Proceedings of IEEE International Workshop on Cellular
Neural Networks and Applications, 1996, pp. 181-186.
[25] Y. Liu, W. Tang, Exponential stability of fuzzy cellular neural networks
with constant and time-varying delays, Phys. Lett. A 323 (2004) 224-233.
[26] K. Yuan, J. Cao, J. Deng, Exponential stability and periodic solutions of
fuzzy cellular neural networks with time-varying delays, Neurocomputing
69 (2006) 1619-1627.
[27] T. Huang, Exponential stability of delayed fuzzy cellular neural networks
with diffusion, Chaos, Solitons and Fractals 31 (2007) 658-664.
[28] S. Mohamad, Global exponential stability in continuous-time and
discrete-time delayed bidirectional neural networks, Physica D 159 (2001)
233-251.
[29] S. Mohamad, K. Gopalsamy, Exponential stability of continuous-time
and discrete-time cellular neural networks with delays, Appl. Math.
Comput. 135 (2003) 17-38.
[30] J.L. Liang, J.D. Cao, D.W.C. Ho, Discrete-time bidirectional associative
memory neural networks with variable delays, Phys. Lett. A 335 (2005)
226-234.
[31] K.L. Mak, J.G. Peng, Z.B. Xu, K.F.C. Yiu, A new stability criterion for
discrete-time neural networks: nonlinear spectral radius, Chaos, Solitons
and Fractals 31 (2007) 424-436.
[32] Q.K. Song, J.D. Cao, Dynamical behaviors of discrete-time fuzzy
cellular neural networks with variable delays and impulses, Journal of
the Franklin Institute 345 (2008) 39-59.