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Delay-dependent asymptotic stability for neural networks with distributed delays. (English) Zbl 1194.34140
The authors consider the neural networks with distributed delays $$u_i(t)= -d_i(u_i(t))+ \sum^n_{j=1} w_{ij} g_j(u_j(t))+ \sum^n_{j=1} w^\tau_{ij} \int^t_{-\infty} K_{ij}(t- s)g_j(u_j(s))\,ds+ I_i,$$ $i= 1,2,\dots, n$. Here $w_{ij}, w^\tau_{ij}$, $I_i$ are real constants. Under assumptions, too lengthy to be stated here, they obtain, by using Lyapunov functionals, local and global asymptotic stability results of the equilibrium.

##### MSC:
 34K20 Stability theory of functional-differential equations 92B20 General theory of neural networks (mathematical biology) 45D05 Volterra integral equations 45M05 Asymptotic theory of integral equations
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