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Dynamic analysis of stochastic bidirectional associative memory neural networks with delays. (English) Zbl 1149.34054

The authors consider the stochastic bidirectional associative memory neural network model with delays

du i (t)=[-c i u i (t)+ j=1 n p ji f j (v j (t-τ j ))+I i ]dt+ j=1 n σ ji (v j (t))dω j (t),dv j (t)=[-d j v j (t)+ i=1 n q ij g j (u i (t-η i ))+J j ]dt+ i=1 n σ ij (u i (t))dω i (t),t0,u i (t)=ξ(t)t,v j (t)=ζ j (t),-τt0,

with n-dimensional driving Brownian motion ω=(ω 1 ,...,ω n ). Sufficient conditions are obtained for a.s. exponential stability, pth order exponential stability, and mean-value exponential stability. Stochastic analysis, Lyapunov functionals, and inequality technique are used.

34K50Stochastic functional-differential equations
34K20Stability theory of functional-differential equations
60H10Stochastic ordinary differential equations
92C40Biochemistry, molecular biology