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Stability of stochastic delay neural networks. (English) Zbl 0991.93120
The stochastically perturbed network with delays \[ dx(t)= \bigl[ -Bx(t)+ Ag\bigl(x_\tau (t)\bigr) \biggr]dt +\sigma\bigl( x(t),x_\tau (t), t\bigr)dw(t), t\geq 0;\;x(s)=\xi(s),\;-\tau\leq s\leq 0;\tag{1} \] is considered. Here \(w(t)\) is an \(m\)-dimensional Brownian motion, \(\sigma(x,y,t)\) is locally Lipschitz continuous and satisfies the linear growth conditions.
Several sufficient criteria are established for almost sure exponential stability of (1).

93E15 Stochastic stability in control theory
92B20 Neural networks for/in biological studies, artificial life and related topics
93C23 Control/observation systems governed by functional-differential equations
Full Text: DOI
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