Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2012 (2012), Article ID 693163, 12 pages.
Exponential Stability for a Class of Stochastic Reaction-Diffusion Hopfield Neural Networks with Delays
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.
J. Appl. Math., Volume 2012 (2012), Article ID 693163, 12 pages.
First available in Project Euclid: 17 October 2012
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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