A new approach to partial synchronization in globally coupled rotators

TL;DR

This paper introduces a formalism for analyzing partial synchronization in pulse-coupled identical oscillators, applying it to LIF neurons, deriving exact delayed equations, and exploring effects of noise and different force fields.

Contribution

A novel formalism for analyzing partial synchronization in pulse-coupled oscillators, with exact delayed equations for LIF neurons and perturbative analysis in weak coupling.

Findings

Exact delayed equations for LIF neuron dynamics in the thermodynamic limit.

Reduction to ordinary differential equations in the weak coupling regime.

Robustness of partial synchronization under noise and varied force fields.

Abstract

We develop a formalism to analyze the behaviour of pulse--coupled identical phase oscillators with a specific attention devoted to the onset of partial synchronization. The method, which allows describing the dynamics both at the microscopic and macroscopic level, is introduced in a general context, but then the application to the dynamics of leaky integrate-and-fire (LIF) neurons is analysed. As a result, we derive a set of delayed equations describing exactly the LIF behaviour in the thermodynamic limit. We also investigate the weak coupling regime by means of a perturbative analysis, which reveals that the evolution rule reduces to a set of ordinary differential equations. Robustness and generality of the partial synchronization regime is finally tested both by adding noise and considering different force fields.