Analysis of the response properties of a computationally efficient spike initiator model

A simple model for neuronal spike initiation is presented. It comprises two linear differential equations and is based on the work of Hill, Rashevsky and Monnier (Rashevsky 1933; Monnier 1934; Hill 1936). Three different versions of the model and the corresponding assumptions are described. The intrinsic noise model used with the deterministic equations is described. The equations are analyzed through the direct solution of relevant equations and the technique of phase plane analysis. The analysis reveals that a subset of the model parameters is responsible for the distinction between spike initiator models which fire a single spike and those that fire repetitively in the presence of a sustained stimulus. Relationships between stimulus intensity and different modes of operation are derived. The effects of the three different versions of the model are compared analytically.