Non-linear excitation theory: Non-accommodative, sub-threshold effects

Abstract

The standard two factor excitation theories should be called “preexcitation” theories since they apply only to those events occurring just up to excitation. A true phenomenological excitation theory which describes thewhole excitation cycle must involve non-linear equations. The nature of these non-linearities is suggested by B. Katz's subthreshold response data. From this data is constructed a “local phenomenological characteristic” which is analogous to the current-voltage characteristic of a non-linear electrical or mechanical system capable of displaying relaxation oscillations. Excitation by constant currents is shown to occur where the slope of the characteristic changes sign. The variation of the time constant of excitation with degree of response, explained by W. A. H. Rushton in terms of a liminal length, is described here in purely formal terms. The theory as presented explicity treats only those events in the excitation cycle up to and a little beyond excitation; the complete excitation cycle (including recovery and repetition) is mentioned as being amenable to mathematical treatment by an extension of the present theory.