Phase synchronization of coupled bursting neurons and the generalized Kuramoto model

TL;DR

This paper explores how coupled bursting neurons synchronize their phases, using a generalized Kuramoto model to analyze the transition from non-synchronization to partial synchronization across different network topologies.

Contribution

It introduces a geometrical phase for bursting neurons and relates their synchronization behavior to a generalized Kuramoto model, providing both numerical and theoretical insights.

Findings

Critical coupling strength for synchronization transition identified.

Comparison between numerical simulations and theoretical predictions.

Synchronization behavior varies with network topology.

Abstract

Bursting neurons fire rapid sequences of action potential spikes followed by a quiescent period. The basic dynamical mechanism of bursting is the slow currents that modulate a fast spiking activity caused by rapid ionic currents. Minimal models of bursting neurons must include both effects. We considered one of these models and its relation with a generalized Kuramoto model, thanks to the definition of a geometrical phase for bursting and a corresponding frequency. We considered neuronal networks with different connection topologies and investigated the transition from a non-synchronized to a partially phase-synchronized state as the coupling strength is varied. The numerically determined critical coupling strength value for this transition to occur is compared with theoretical results valid for the generalized Kuramoto model.