Analysis of Interspike-Intervals for the General Class of Integrate-and-Fire Models with Periodic Drive

Abstract

We study one-dimensional integrate-and-fire models of the general type x˙ = F(t, x) and analyze properties of the firing map which iterations recover consecutive spike timings. We impose very week constraints for the regularity of the function F(t, x), e.g. often it suffices to assume that F is continuous. If additionally F is periodic in t, using mathematical study of the displacement sequence of an orientation preserving circle homeomorphism, we provide a detailed description of the regularity properties of the sequence of interspike-intervals and behaviour of the interspike-interval distribution.

Keyword : integrate-and-fire neuron, firing map, interspike intervals, ordinary differential equations, circle maps