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Zbl 1058.34007
Akça, Haydar; Alassar, Rajai; Covachev, Valéry; Covacheva, Z.
Discrete counterparts of continuous-time additive Hopfield-type neural networks with impulses. (English)
[J] Dyn. Syst. Appl. 13, No. 1, 77-92 (2004). ISSN 1056-2176

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 $k=1,2,\dots ,$\par $\Delta x(t_k)=x(t_k+0)-x(t_k-0)$ are the impulses at the moment $t_k.$ The authors give also a discrete-time formulation. Furthermore, the authors establish conditions for global stability.
[Wan-Tong Li (Lanzhou)]

MSC 2000:: *34A37 Differential equations with impulses
34D23 Global stability
39A11 Stability of difference equations
92B20 General theory of neural networks

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

Cited in: Zbl 1122.92001

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