Kuramoto model for populations of quadratic integrate-and-fire neurons with chemical and electrical coupling

TL;DR

This paper derives a Kuramoto model for weakly coupled quadratic integrate-and-fire neurons with chemical and electrical interactions, revealing how coupling ratios influence synchronization and chimera states.

Contribution

It introduces a novel derivation of the Kuramoto model tailored for QIF neurons with dual coupling types, linking coupling ratios to network dynamics.

Findings

Chemical to electrical coupling ratio affects phase lag and synchronization.

Chimera states require both electrical and chemical coupling to exist.

Chimera states diminish as coupling strength increases beyond weak coupling.

Abstract

We derive the Kuramoto model (KM) corresponding to a population of weakly coupled, nearly identical quadratic integrate-and-fire (QIF) neurons with both electrical and chemical coupling. The ratio of chemical to electrical coupling determines the phase lag of the characteristic sine coupling function of the KM and critically determines the synchronization properties of the network. We apply our results to investigate chimera states in two coupled populations of identical QIF neurons. We find that the presence of both electrical and chemical coupling is a necessary condition for chimera states to exist. Finally, we numerically demonstrate that chimera states gradually disappear as coupling strengths cease to be weak.