Relaxation cycles of the generalized pulsed neuron equation

I. V. Paramonov

P. G. Demidov Yaroslavl State University

Abstract: In the paper we analyze the generalized model of the V. V. Mayorov and I. Yu. Myshkin pulsed neuron. The neuron equation contains a delay of the sodium conductance with respect to the transmembrane potential as well as the potassium one. We proved the exisence and stability of the periodic solution and obtained its asymptotic expansion.

Keywords: relaxation oscillations; pulsed neuron; differential-difference equation; asymptotic analysis.

UDC: 517.9

Received: 17.10.2010