Stability of stochastic delay neural networks. (English) Zbl 0991.93120

Blythe, Steve; Mao, Xuerong; Liao, Xiaoxin

J. Franklin Inst. 338, No. 4, 481-495 (2001).

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).

Reviewer: Alexandra Rodkina (Mona, Kingston)

MSC:

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

Keywords:

stochastic stability; delay neural network; martingale convergence theorem; random disturbance; sufficient criteria; almost sure exponential stability

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