First-order synchronization transition in a large population of strongly coupled relaxation oscillators

TL;DR

This study demonstrates a first-order, discontinuous synchronization transition with hysteresis in strongly coupled relaxation oscillators, contrasting with the traditional continuous transition predicted by weak coupling theory.

Contribution

It reveals that the relaxation character of oscillators fundamentally determines the nature of the synchronization transition, supported by experimental evidence and mechanistic insights.

Findings

Discontinuous synchronization transition with hysteresis observed

Transition robustness across network connectivity and frequency distributions

Relaxation character identified as key parameter

Abstract

Onset and loss of synchronization in coupled oscillators are of fundamental importance in understanding emergent behavior in natural and man-made systems, which range from neural networks to power grids. We report on experiments with hundreds of strongly coupled photochemical relaxation oscillators that exhibit a discontinuous synchronization transition with hysteresis, as opposed to the paradigmatic continuous transition expected from the widely used weak coupling theory. The resulting first-order transition is robust with respect to changes in network connectivity and natural frequency distribution. This allows us to identify the relaxation character of the oscillators as the essential parameter that determines the nature of the synchronization transition. We further support this hypothesis by revealing the mechanism of the transition, which cannot be accounted for by standard phase reduction techniques.