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Zbl 0991.93120
Blythe, Steve; Mao, Xuerong; Liao, Xiaoxin
Stability of stochastic delay neural networks. (English)
[J] J. Franklin Inst. 338, No.4, 481-495 (2001). ISSN 0016-0032; ISSN 1879-2693/e

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.\par Several sufficient criteria are established for almost sure exponential stability of (1).
[Alexandra Rodkina (Mona, Kingston)]

MSC 2000:: *93E15 Stochastic stability
92B20 General theory of neural networks
93C23 Systems governed by functional-differential equations

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

Cited in: Zbl 1109.92003

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