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Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays. (English) Zbl 1062.68102

Summary: First, convergence of continuous-time Bidirectional Associative Memory (BAM) neural networks are studied. By using Lyapunov functionals and some analysis technique, delay-independent sufficient conditions are obtained for the networks to converge exponentially toward the equilibrium associated with the constant input sources. Second, discrete-time analogues of the continuous-time BAM networks are formulated and studied. It is shown that the convergence characteristics of the continuous-time systems are preserved by the discrete-time analogues without any restriction imposed on the uniform discretionary step size. An illustrative example is given to demonstrate the effectiveness of the obtained results.

MSC:

68T05 Learning and adaptive systems in artificial intelligence
34K20 Stability theory of functional-differential equations
93D30 Lyapunov and storage functions
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[1] Kosko, B., (Neural networks and fuzzy systems-a dynamical system approach machine intelligence (1992), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ), 38-108 · Zbl 0755.94024
[2] Kosko, B., Adaptive bi-directional associative memories, Appl. Opt., 26, 23, 4947-4960 (1987)
[3] Kosko, B., Bi-directional associative memories, IEEE Trans. Syst. Man Cybernet., 18, 1, 49-60 (1988)
[4] Gopalsamy, K.; He, X. Z., Delay-independent stability in bi-directional associative memory networks, IEEE Trans. Neural Networks, 5, 998-1002 (1994)
[5] Mohamad, S., Global exponential stability in continuous-time and discrete-time delay bidirectional neural networks, Physica D, 159, 233-251 (2001) · Zbl 0984.92502
[6] Chen, A. P.; Hang, L. H.; Cao, J., Existence and stability of almost periodic solution for BAM neural networks with delays, Appl. Math. Comput., 137, 1, 177-193 (2003) · Zbl 1034.34087
[7] Cao, J.; Dong, M., Exponential stability of delayed bidirectional associative memory networks, Appl. Math. Comput., 135, 105-112 (2003) · Zbl 1030.34073
[8] Cao, J.; Wang, L., Periodic oscillatory solution of bidirectional associative memory networks with delays, Phys. Rev. E, 61, 2, 1825-1828 (2000)
[9] Zhang, Y.; Yang, Y. R., Global stability analysis of bi-directional associative memory neural networks with time delay, Int. J. Circ. Theor. Appl., 29, 185-196 (2001) · Zbl 1001.34066
[10] Liao, X. F.; Liu, G. Y.; Yu, J. B., Neural networks of bi-direcional associative memory with axonal signal transmission delays, J. Electron., 19, 4, 439-444 (1997), [in Chinese]
[11] Michel, A. N.; Farrell, J. A.; Porod, W., Qualitative analysis of neurqal networks, IEEE Trans. Circuits Syst., 36, 2, 229-243 (1989) · Zbl 0672.94015
[12] Liao, X. F.; Yu, J. B., Qualitative analysis of bi-directional associative memory with time delays, Int. J. Circuit Theory Appl., 26, 3, 219-229 (1998) · Zbl 0915.94012
[13] Forti, M.; Tesi, A., New conditions for global stability of neural networks with application to linear and quadratic programming problems, IEEE Trans. Circuits Syst.–I: Fundam. Theory Appl., 42, 7, 354-366 (1995) · Zbl 0849.68105
[14] Cao, J.; Wang, L., Exponential stability and periodic oscillatory solution in BAM networks with delays, IEEE Trans. Neural Networks, 13, 2, 457-463 (2002)
[15] Yang, H.; Dillon, T. S., Exponential stability and oscillation of Hopfield graded response neural networks, IEEE Trans. Neural Networks, 5, 719-729 (1994)
[16] Zhang, Y., Qualitative analysis of bi-directional associative memory neural networks with delays, J. Comput. Res. Dev., 36, 2, 150-155 (1999), [in Chinese]
[17] Zhao, H. Y., Global stability of bi-directional associative memory neural networks with distributed delays, Phys. Lett. A, 297, 3-4, 182-190 (2002) · Zbl 0995.92002
[18] Cao, J., Global asymptotic stability of delayed bi-directional associative memory neural networks, Appl. Math. Comput., 142, 333-339 (2003) · Zbl 1031.34074
[19] Cao, J.; Wang, J., Global asymptotic stability of a general class of recurrent neural networks with time-varying delays, IEEE Trans. Circuits Syst. I, 50, 1, 34-44 (2003) · Zbl 1368.34084
[20] Cao, J.; Wang, J., Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays, Neural Networks, 17, 3, 379-390 (2004) · Zbl 1074.68049
[21] Cao, J.; Wang, J.; Liao, X., Novel stability criteria of delayed cellular neural networks, Inter. J. Neural Syst., 13, 5, 367-375 (2003)
[22] Cao, J., Exponential stability and periodic solution of delayed cellular neural networks, Science in China (Series E), 43, 3, 328-336 (2000) · Zbl 1019.94041
[23] Chen, A.; Cao, J.; Huang, L., Exponential stability of BAM neural networks with transmission delays, Neurocomputing, 57, 435-454 (2004)
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