A modification of the Hodgkin–Huxley model and a mathematical interpretation of the principal neurophysiological “all-or-none” law

In the paper we present the results of numerical simulation for the simplified and modified Hodgkin–Huxley model of primary afferent neuron in the presence of stochastic noise. The transitions from the attraction domain of the stationary point — the stable focus — to the attraction domain of the periodic attractor and back to the attraction domain of the focus are considered. Such transitions can alternate many times, which is the mathematical interpretation of the principal neurophysiological all-or-none law.