Fixed points and exponential stability for a stochastic neutral cellular neural network. (English) Zbl 1315.34087
Summary: We study the stability of a stochastic neutral cellular neural network
\[
\begin{aligned} d[x(t)-cx(t-{\tau}_1)]=& [-(A+\bigtriangleup A(t))x(t)+f(t,x(t),x(t-{\tau}_2))]dt\\ & +{\sigma}(t,x(t),x(t-{\tau}_3))dw(t).\end{aligned}
\]
By using fixed point theory, we obtain new criteria for exponential stability in mean square of the considered stochastic neutral cellular neural network. Finally, an example is provided to illustrate the relevance of the results.
MSC:
| 34K50 | Stochastic functional-differential equations |
| 34K40 | Neutral functional-differential equations |
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
| 47N20 | Applications of operator theory to differential and integral equations |
| 34K20 | Stability theory of functional-differential equations |
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