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Mean square exponential stability of stochastic delayed Hopfield neural networks. (English) Zbl 1194.37186

Summary: Stochastic effects to the stability property of Hopfield neural networks (HNN) with discrete and continuously distributed delay are considered. By using the method of variation parameter, inequality technique and stochastic analysis, the sufficient conditions to guarantee the mean square exponential stability of an equilibrium solution are given. Two examples are also given to demonstrate our results.

MSC:

37N99 Applications of dynamical systems
37H99 Random dynamical systems
68T05 Learning and adaptive systems in artificial intelligence
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[1] Arik, S., IEEE trans. neural networks, 13, 5, 1239, (2002)
[2] Arik, S., IEEE trans. circuits systems I, 49, 8, 1211, (2002)
[3] Arik, S., IEEE trans. circuits systems I, 50, 1, 156, (2003)
[4] Arnold, L., Stochastic differential equations: theory and applications, (1972), Wiley New York
[5] Blythe, S.; Mao, X.; Liao, X., J. franklin inst., 338, 481, (2001)
[6] Buhmann, J.; Schulten, K., Biol. cybernet., 56, 313, (1987)
[7] Cao, J., IEEE trans. circuits systems I, 48, 11, 1330, (2001)
[8] Cao, J.; Wang, J., IEEE trans. circuits systems I, 50, 1, 34, (2003)
[9] Cao, J., Phys. lett. A, 307, 136, (2003)
[10] Chen, T.; Amari, S., IEEE trans. neural networks, 12, 1, 159, (2001)
[11] Chen, T., Neural networks, 14, 3, 251, (2001)
[12] Chen, Y., Neural networks, 15, 867, (2002)
[13] Chua, Leon O.; Yang, L., IEEE trans. circuits systems, 35, 10, 1273, (1988)
[14] Chua, Leon O.; Yang, L., IEEE trans. circuits systems, 35, 10, 1257, (1988)
[15] Chua, Leon O.; Roska, T., IEEE trans. circuits systems I, 40, 3, 147, (1993)
[16] Le Cun, Y.; Galland, C.C.; Hinton, G.E., GEMINI: gradient estimation through matrix inversion after noise injection, (), 138-141
[17] Friedman, A., Stochastic differential equations and applications, (1976), Academic Press New York
[18] Gopalsamy, K.; He, X., Physica D, 76, 344, (1994)
[19] Haykin, S., Neural networks, (1994), Prentice-Hall Englewood Cliffs, NJ · Zbl 0828.68103
[20] Hopfield, J.J., Proc. natl. acad. sci. USA, 79, 2254, (1982)
[21] Hopfield, J.J., Proc. natl. acad. sci. USA, 81, 3088, (1984)
[22] Hopfield, J.J.; Tank, D.W., Model sci., 233, 3088, (1986)
[23] Horn, R.A.; Johnson, C.R., Matrix analysis, (1985), Cambridge Univ. Press London · Zbl 0576.15001
[24] Liao, X., Absolute stability of nonlinear control systems, (1993), Kluwer Dordrecht
[25] Liao, X.; Mao, X., Stochast. anal. appl., 14, 2, 165, (1996)
[26] Liao, X.; Mao, X., Neural, parallel sci. comput., 4, 2, 205, (1996) · Zbl 1060.92502
[27] Maass, W.; Bishop, C.M., Pulsed neural networks, (1999), MIT Press Cambridge, MA
[28] Mao, X., Stochastic differential equations and applications, (1997), Ellis Horwood · Zbl 0874.60050
[29] Mohamad, S.; Gopalsamy, K., Math. comput. simul., 53, 1, (2000)
[30] Quezz, A.; Protoposecu, V.; Barben, J., IEEE trans. systems man cybernet., 18, 80, (1983)
[31] Sree Hari Rao, V.; Phaneendra, Bh.R.M., Neural networks, 12, 445, (1999)
[32] Zhang, Y.; Heng, A.; Vadakkepat, P., IEEE trans. circuits systems I, 49, 2, 256, (2002)
[33] Zhang, J.; Jin, X., Neural networks, 13, 745, (2000)
[34] Zhang, Q.; Ma, R.; Xu, J., Commun. theor. phys., 39, 381, (2003)
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