Discrete counterparts of continuous-time additive Hopfield-type neural networks with impulses. (English) Zbl 1058.34007

Akça, Haydar; Alassar, Rajai; Covachev, Valéry; Covacheva, Z.

Dyn. Syst. Appl. 13, No. 1, 77-92 (2004).

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.

Reviewer: Wan-Tong Li (Lanzhou)

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