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Stability of stochastic delay neural networks. (English) Zbl 0991.93120
The stochastically perturbed network with delays $$dx(t)= \bigl[ -Bx(t)+ Ag\bigl(x_\tau (t)\bigr) \biggr]dt +\sigma\bigl( x(t),x_\tau (t), t\bigr)dw(t), t\ge 0;\ x(s)=\xi(s),\ -\tau\le s\le 0;\tag 1$$ 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).

93E15Stochastic stability
92B20General theory of neural networks (mathematical biology)
93C23Systems governed by functional-differential equations
Full Text: DOI
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