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Zbl 1149.34054
Zhao, Hongyong; Ding, Nan
Dynamic analysis of stochastic bidirectional associative memory neural networks with delays. (English)
[J] Chaos Solitons Fractals 32, No. 5, 1692-1702 (2007). ISSN 0960-0779

The authors consider the stochastic bidirectional associative memory neural network model with delays $$ \cases du_i(t)=[-c_iu_i(t)+\sum_{j=1}^np_{ji}f_j(v_j(t-\tau_j))+I_i]\,dt +\sum_{j=1}^n\sigma_{ji}(v_j(t))\,d\omega_j(t),\\ dv_j(t)=[-d_jv_j(t)+\sum_{i=1}^nq_{ij}g_j(u_i(t-\eta_i))+J_j]\,dt +\sum_{i=1}^n\sigma_{ij}(u_i(t))\,d\omega_i(t),\quad t\ge0,\\u_i(t)=\xi(t)t,\quad v_j(t)=\zeta_j(t),\quad -\tau\le t\le0,\endcases $$ 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.
[Vigirdas Mackevičius (Vilnius)]

MSC 2000:: *34K50 Stochastic delay equations
34K20 Stability theory of functional-differential equations
60H10 Stochastic ordinary differential equations
92C40 Biochemistry, etc.
92D10 Genetics

Keywords: neural network; Lyapunov functional; exponential stability

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