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

Liang, Jinling; Cao, Jinde

Chaos Solitons Fractals 22, No. 4, 773-785 (2004).

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

Keywords:

Lyapunov functionals

References:

[1]	Kosko, B., (), 38-108
[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)