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Discrete counterparts of continuous-time additive Hopfield-type neural networks with impulses. (English) Zbl 1058.34007
The paper studies the following Hopfield-type model of a neural network with impulses \[ \frac{dx_i}{dt}=-a_ix_i(t)+\sum_{j=1}^mb_{ij}f_j(x_j(t))+c_i \] with \(\Delta x_i(t_k)=I_i(x_i(t_k))\) where \(t>0,\) \(t\neq t_k,i=1,\dots,m\), and \(k=1,2,\dots ,\)
\(\Delta x(t_k)=x(t_k+0)-x(t_k-0)\) are the impulses at the moment \(t_k.\) The authors give also a discrete-time formulation. Furthermore, the authors establish conditions for global stability.

MSC:
34A37 Ordinary differential equations with impulses
34D23 Global stability of solutions to ordinary differential equations
39A11 Stability of difference equations (MSC2000)
92B20 Neural networks for/in biological studies, artificial life and related topics
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