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Global asymptotic stability of uncertain stochastic bi-directional associative memory networks with discrete and distributed delays. (English) Zbl 1195.34125
The authors study a class of stochastic delay differential equations (SDDEs) driven by Brownian motion which are used to model a bi-directional associative memory network. They establish a sufficient criterion for mean-square stability of the trivial solution in terms of the validity of four matrix inequalities involving matrices which are functions of the coefficients of the SDDE. To prove the result, the authors construct a suitable Lyapunov-Krasovskii function.

MSC:
34K50 Stochastic functional-differential equations
90B15 Stochastic network models in operations research
92B20 Neural networks for/in biological studies, artificial life and related topics
93E15 Stochastic stability in control theory
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
Software:
Matlab; LMI toolbox
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