Journal of Applied Mathematics

Exponential Stability for a Class of Stochastic Reaction-Diffusion Hopfield Neural Networks with Delays

Xiao Liang and Linshan Wang

Full-text: Open access

Abstract

This paper studies the asymptotic behavior for a class of delayed reaction-diffusion Hopfield neural networks driven by finite-dimensional Wiener processes. Some new sufficient conditions are established to guarantee the mean square exponential stability of this system by using Poincaré’s inequality and stochastic analysis technique. The proof of the almost surely exponential stability for this system is carried out by using the Burkholder-Davis-Gundy inequality, the Chebyshev inequality and the Borel-Cantelli lemma. Finally, an example is given to illustrate the effectiveness of the proposed approach, and the simulation is also given by using the Matlab.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 693163, 12 pages.

Dates
First available in Project Euclid: 17 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1350479386

Digital Object Identifier
doi:10.1155/2012/693163

Mathematical Reviews number (MathSciNet)
MR2898077

Zentralblatt MATH identifier
1244.93121

Citation

Liang, Xiao; Wang, Linshan. Exponential Stability for a Class of Stochastic Reaction-Diffusion Hopfield Neural Networks with Delays. J. Appl. Math. 2012 (2012), Article ID 693163, 12 pages. doi:10.1155/2012/693163. https://projecteuclid.org/euclid.jam/1350479386


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