Geodesic
Relaxation self-oscillations in Hopfield networks with delay
Izvestiya. Mathematics , Tome 77 (2013) no. 2, pp. 271-312.

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We consider two singularly perturbed non-linear systems of differential-difference equations with delay; one of them is a mathematical model of a single Hopfield neuron and the other simulates the functioning of a circular network of three or more neurons connected unidirectionally. We study the problems of existence, asymptotic behaviour, and stability for these systems of relaxation periodic motions.
Keywords: differential-difference equations, Hopfield neuron networks, relaxation cycle, stability, buffer property. 
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S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. Relaxation self-oscillations in Hopfield networks with delay. Izvestiya. Mathematics , Tome 77 (2013) no. 2, pp. 271-312. http://geodesic.mathdoc.fr/item/IM2_2013_77_2_a2/

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