Generalized Phase Representation of Integrate-and-Fire Models

TL;DR

This paper derives a general phase model representation for all integrate-and-fire neuron models, elucidating conditions for Type-II neuron firing behavior and improving analysis and simulation methods.

Contribution

It introduces a unified phase model framework for integrate-and-fire neurons and identifies conditions for discontinuous firing rate onset.

Findings

Derived the general phase model expression for all integrate-and-fire models.

Identified conditions for discontinuous onset firing rate in phase models.

Enhanced understanding of Type-II neuron dynamics.

Abstract

The quadratic integrate-and-fire (QIF) model captures the normal form bifurcation dynamics of Type-I neurons found in cortex. Remarkably, this model is known to have a dual equivalent representation in terms of phase, called the $\theta$-model, which has advantages for numerical simulations and analysis over the QIF model. Here, I investigate the nature of the dual representation and derive the general phase model expression for all integrate-and-fire models. Moreover, I show the condition for which the phase models exhibit discontinuous onset firing rate, the hallmark of Type-II spiking neurons.