An organizing center in a planar model of neuronal excitability

TL;DR

This paper analyzes a generalized FitzHugh-Nagumo model incorporating cooperative gating variables, revealing a bifurcation structure that organizes classical and novel neuronal excitability types.

Contribution

It introduces a bifurcation framework for understanding five excitability types, including two newly identified due to cooperative variables.

Findings

Identifies five excitability types organized by a pitchfork bifurcation.

Describes two novel excitability types linked to cooperative gating variables.

Provides a unified bifurcation perspective on neuronal excitability.

Abstract

The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating variables such as activation of calcium currents. Excitability is explored by unfolding a pitchfork bifurcation that is shown to organize five different types of excitability. In addition to the three classical types of neuronal excitability, two novel types are described and distinctly associated to the presence of cooperative variables.