A Modification of the Hodgkin–Huxley Model and a Mathematical Interpretation of the Principal Neurophysiological ‘‘All-or-None’’ Law

Abstract

The paper presents the results of simulation with the simplified modified Hodgkin–Huxley model of an afferent primary neuron in the presence of stochastic noise. The transition from the attraction domain of a point attractor like a stable focus to the attraction domain of a periodic attractor and the inverse transition to the attraction domain of the point attractor are considered. Some examples, in which such transitions may be repeatedly alternated, have been obtained as a mathematical interpretation of the principal neurophysiological ‘‘all-or-none’’ law.