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

Authors: Chao Wang, Yongkun Li

Abstract:

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.

Keywords: Discrete-time fuzzy BAM neural networks, ımpulses, global exponential stability, global asymptotical stability, equilibrium point.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1333913

References:

[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.