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Attractor and ultimate boundedness for stochastic cellular neural networks with delays. (English) Zbl 1225.34091
Summary: This paper investigates attractors and ultimate boundedness of stochastic cellular neural networks with delays. By employing the Lyapunov method and a Lasalle-type theorem, novel results and sufficient criteria for the existence of an attractor and ultimate boundedness are obtained.

MSC:
34K50 Stochastic functional-differential equations
34K12 Growth, boundedness, comparison of solutions to functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
34K25 Asymptotic theory of functional-differential equations
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[1] Roska, T.; Chua, L., Cellular neural networks with nonlinear and delay-type template elements, Int. J. circuit theory appl., 20, 469-481, (1992) · Zbl 0775.92011
[2] Liu, D.; Michel, A.N., Cellular neural networks for associative memories, IEEE trans. circuits syst. I, 40, 119-121, (1993) · Zbl 0800.92046
[3] 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, 42, 354-366, (1995) · Zbl 0849.68105
[4] Huang, C.; Cao, J., Almost sure exponential stability of stochastic cellular neural networks with unbounded distributed delays, Neurocomputing, 72, 3352-3356, (2009)
[5] Huang, C.; Cao, J., On \(p\)th moment exponential stability of stochastic cohen – grossberg neural networks with time-varying delays, Neurocomputing, 73, 986-990, (2010)
[6] Huang, C.; Chen, P.; He, Y.; Huang, L.; Tan, W., Almost sure exponential stability of delayed Hopfield neural networks, Appl. math. lett., 21, 701-705, (2008) · Zbl 1152.34372
[7] Huang, C.X.; He, Y.G.; Huang, L.H.; Zhu, W.J., \(p\)th moment stability analysis of stochastic recurrent neural networks with time-varying delays, Inform. sci., 178, 2194-2203, (2008) · Zbl 1144.93030
[8] Huang, C.; He, Y.; Wang, H., Mean square exponential stability of stochastic recurrent neural networks with time-varying delays, Comput. math. appl., 56, 1773-1778, (2008) · Zbl 1152.60346
[9] Rakkiyappan, R.; Balasubramaniam, P., Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays, Appl. math. comput., 198, 526-533, (2008) · Zbl 1144.34375
[10] Sun, Y.; Cao, J., \(p\)th moment exponential stability of stochastic recurrent neural networks with time-varying delays, Nonlinear anal. RWA, 8, 1171-1185, (2007) · Zbl 1196.60125
[11] Song, Q.; Wang, Z., Stability analysis of impulsive stochastic cohen – grossberg neural networks with mixed time delays, Physica A, 387, 3314-3326, (2008)
[12] Wang, Z.; Fang, J.; Liu, X., Global stability of stochastic high-order neural networks with discrete and distributed delays, Chaos solitons fractals, 36, 388-396, (2008) · Zbl 1141.93416
[13] Zhao, H.; Ding, N., Dynamic analysis of stochastic bidirectional associative memory neural networks with delays, Chaos solitons fractals, 32, 1692-1702, (2007) · Zbl 1149.34054
[14] Zhao, H.; Ding, N.; Chen, L., Almost sure exponential stability of stochastic fuzzy cellular neural networks with delays, Chaos solitons fractals, 40, 1653-1659, (2009) · Zbl 1198.34173
[15] Chen, W.H.; Lu, X.M., Mean square exponential stability of uncertain stochastic delayed neural networks, Phys. lett. A, 372, 7, 1061-1069, (2008) · Zbl 1217.92005
[16] Huang, H.; Feng, G., Delay-dependent stability for uncertain stochastic neural networks with time-varying delay, Physica A, 381, 15, 93-103, (2007)
[17] Zhang, J.; Shi, P.; Qiu, J., Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays, Nonlinear anal. RWA, 8, 4, 1349-1357, (2007) · Zbl 1124.34056
[18] Mao, X.R., Stochastic differential equations and applications, (1997), Horwood Publishing
[19] Mao, X.R., A note on the Lasalle-type theorems for stochastic differential delay equations, J. math. anal. appl., 268, 125-142, (2002) · Zbl 0996.60064
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