Tuning synchronization of integrate-and-fire oscillators through mobility

TL;DR

This paper investigates how the movement speed of integrate-and-fire oscillators affects their synchronization, revealing complex dependencies and different mechanisms across regimes, with implications for controlling collective dynamics.

Contribution

It introduces a model of moving oscillators interacting locally and analyzes how their velocity influences synchronization, identifying distinct dynamical regimes and transition estimators.

Findings

Synchronization time varies non-monotonically with velocity

Different mechanisms dominate in different dynamical regimes

High mobility can inhibit synchronization entirely

Abstract

We analyze the emergence of synchronization in a population of moving integrate-and-fire oscillators. Oscillators, while moving on a plane, interact with their nearest neighbor upon firing time. We discover a non-monotonic dependence of the synchronization time on the velocity of the agents. Moreover, we find that mechanisms that drive synchronization are different for different dynamical regimes. We report the extreme situation where an interplay between the time-scales involved in the dynamical processes completely inhibit the achievement of a coherent state. We also provide estimators for the transitions between the different regimes.