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Mean square exponential stability of stochastic neural networks with reaction-diffusion terms and delays. (English) Zbl 1213.93200
Summary: Some sufficient conditions ensuring mean square exponential stability of the equilibrium point of a class of stochastic neural networks with reaction-diffusion terms and time-varying delays are obtained. The conditions involving the effect of diffusion terms reduce the conservatism of the previous results. Finally, we give a numerical example to verify the effectiveness of our results.
MSC:
93E12System identification (stochastic systems)
92B20General theory of neural networks (mathematical biology)
34K40Neutral functional-differential equations
References:
[1]Leon O. Chua, CNN: A Paradigm for Complexity, in: World Scientific on Nonlinear Science, series A, vol. 31, Singapore, 1998. · Zbl 0916.68132
[2]Arki, S.; Tavsanoglu, V.: Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays, Neurocomputing 68, 161-176 (2005)
[3]Civalleri, P.; Gill, L.; Pandolfi, L.: On stability of cellular neural networks with delay, IEEE transactions on circuits and systems-I 40, No. 3, 157-164 (1993) · Zbl 0792.68115 · doi:10.1109/81.222796
[4]Zhang, J.; Suda, Y.; Komine, H.: Global exponential stability of Cohen–Grossberg neural networks with variable delays, Physics letter A 338, No. 1, 44-50 (2005) · Zbl 1136.34347 · doi:10.1016/j.physleta.2005.02.005
[5]Li, C.; Liao, X.; Zhang, R.: A global exponential robust stability criterion for interval delayed neural networks with variable delays, Neurocomputing 69, 803-809 (2006)
[6]Allegretto, W.; Papini, D.: Stability for delayed reaction–diffusion neural networks, Physics letters A 360, 669-680 (2007)
[7]Wang, L.; Gao, Y.: Global exponential robust stability of reaction–diffusion interval neural networks with time-varying delays, Physics letters A 350, 342-348 (2006) · Zbl 1195.35179 · doi:10.1016/j.physleta.2005.10.031
[8]Liang, J.; Cao, J.: Global exponential stability of reaction–diffusion recurrent neural networks with time-varying delays, Physics letters A 314, 434-442 (2003) · Zbl 1052.82023 · doi:10.1016/S0375-9601(03)00945-9
[9]Wan, L.; Zhou, Q.: Exponential stability of stochastic reaction–diffusion Cohen–Grossberg neural networks with delays, Applied mathematics and computation 206, 818-824 (2008)
[10]Zhang, Y.; Luo, Q.; Lai, X.: Stability in mean of partial variables for stochastic reaction diffusion systems, Nonlinear analysis 71, 550-559 (2009)
[11]Lu, J.: Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions, Chaos, solitons and fractals 35, 116-125 (2008) · Zbl 1134.35066 · doi:10.1016/j.chaos.2007.05.002
[12]S. Bao, Exponential stability of reaction–diffusion Cohen–Grossberg neural networks with variable coefficients and distributed delays, in: Proceedings of the 7th World Congress on Intelligent Control and Automation, China, 2008, pp. 8261–8264.
[13]Zhou, Q.; Wan, L.: Exponential stability of stochastic delayed Hopfield neural networks, Applied mathematics and computation 199, 84-89 (2008) · Zbl 1144.34389 · doi:10.1016/j.amc.2007.09.025
[14]Li, B.; Xu, D.: Mean square asymptotic behavior of stochastic neural networks with infinitely distributed delays, Neurocomputing 72, 3311-3317 (2009)