Dynamics of a network of quadratic integrate-and-fire neurons with bimodal heterogeneity

TL;DR

This paper derives a low-dimensional mean-field model for a large network of quadratic integrate-and-fire neurons with bimodal heterogeneity, revealing complex dynamics like multistability, oscillations, and chaos.

Contribution

It introduces an exact mean-field framework for bimodal heterogeneity in neuron networks, uncovering new dynamic behaviors not seen with unimodal distributions.

Findings

Bifurcation analysis reveals multistable states and oscillations.

Oscillatory modes coexist with stable equilibrium states.

Mean field equations accurately approximate large-scale neuron models.

Abstract

An exact low-dimensional system of mean-field equations for an infinite-size network of pulse coupled integrate-and-fire neurons with a bimodal distribution of an excitability parameter is derived. Bifurcation analysis of these equations shows a rich variety of dynamic modes that do not exist with a unimodal distribution of this parameter. New modes include multistable equilibrium states with different levels of the spiking rate, collective oscillations and chaos. All oscillatory modes coexist with stable equilibrium states. The mean field equations are a good approximation to the solutions of a microscopic model consisting of several thousand neurons.