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Stability of stochastic reaction-diffusion recurrent neural networks with unbounded distributed delays. (English) Zbl 1214.93088
Summary: Stability of reaction-diffusion Recurrent Neural Networks (RNNs) with continuously distributed delays and stochastic influence are considered. Some new sufficient conditions to guarantee the almost sure exponential stability and mean square exponential stability of an equilibrium solution are obtained, respectively. Lyapunov’s functional method, M-matrix properties, some inequality technique, and nonnegative semimartingale convergence theorem are used in our approach. The obtained conclusions improve some published results.
MSC:
93D20Asymptotic stability of control systems
60H30Applications of stochastic analysis
35K57Reaction-diffusion equations