## Exponential stability for a class of stochastic reaction-diffusion Hopfield neural networks with delays.(English)Zbl 1244.93121

Summary: 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.

### MSC:

 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93E20 Optimal stochastic control 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 92B20 Neural networks for/in biological studies, artificial life and related topics

Matlab
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### References:

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