# zbMATH — the first resource for mathematics

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
##### Keywords:
Hopfield-type neural networks; impulses; global stability