Self-excited relaxation oscillations in networks of impulse neurons

S. D. Glyzin ; A. Yu. Kolesov ; N. Kh. Rozov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 3, pp. 383-452

Résumé

This paper addresses the problem of mathematical modelling of neuron activity. New classes of singularly perturbed differential-difference equations with Volterra-type delay are proposed and used to describe how single neurons and also neural networks function with various kinds of connections (electrical or chemical). Special asymptotic methods are developed which make it possible to analyse questions of the existence and stability of relaxation periodic motions in such systems. Bibliography: 56 titles.

Détail

Keywords: neuron models, differential-difference equations, asymptotic behaviour, stability, buffering, bursting effect.
Mots-clés : relaxation oscillations

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