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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 \[ \begin{cases} du_i(t)=[-c_iu_i(t)+\sum_{j=1}^np_{ji}f_j(v_j(t-\tau_j))+I_i]\,dt +\sum_{j=1}^n\sigma_{ji}(v_j(t))\,d\omega_j(t),\\ dv_j(t)=[-d_jv_j(t)+\sum_{i=1}^nq_{ij}g_j(u_i(t-\eta_i))+J_j]\,dt +\sum_{i=1}^n\sigma_{ij}(u_i(t))\,d\omega_i(t),\quad t\geq0,\\u_i(t)=\xi(t)t,\quad v_j(t)=\zeta_j(t),\quad -\tau\leq t\leq0,\end{cases} \] with \(n\)-dimensional driving Brownian motion \(\omega=(\omega_1,\ldots,\omega_n)\). Sufficient conditions are obtained for a.s. exponential stability, \(p\)th order exponential stability, and mean-value exponential stability. Stochastic analysis, Lyapunov functionals, and inequality technique are used.

MSC:

34K50 Stochastic functional-differential equations
34K20 Stability theory of functional-differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
92C40 Biochemistry, molecular biology
92D10 Genetics and epigenetics
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