Topological Speed Limits to Network Synchronization

TL;DR

This paper investigates how the structure of asymmetric random networks influences the speed of synchronization among pulse-coupled oscillators, revealing fundamental speed limits and robustness properties.

Contribution

It introduces a novel application of random matrix theory to predict synchronization speed limits in asymmetric networks, highlighting the impact of network connectivity.

Findings

Synchronization speed is limited by network connectivity.

Speed remains finite even with infinite coupling strength.

Synchronization is robust to structural perturbations.

Abstract

We study collective synchronization of pulse-coupled oscillators interacting on asymmetric random networks. We demonstrate that random matrix theory can be used to accurately predict the speed of synchronization in such networks in dependence on the dynamical and network parameters. Furthermore, we show that the speed of synchronization is limited by the network connectivity and stays finite, even if the coupling strength becomes infinite. In addition, our results indicate that synchrony is robust under structural perturbations of the network dynamics.