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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 Neural networks for/in biological studies, artificial life and related topics
45D05 Volterra integral equations
45M05 Asymptotics of solutions to integral equations
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