Strong coupling yields abrupt synchronization transitions in coupled oscillators

TL;DR

This paper investigates how increasing coupling strength in oscillator networks leads to abrupt synchronization transitions, highlighting limitations of phase-only models and demonstrating these phenomena through theory and experiments.

Contribution

It systematically analyzes synchronization transitions across coupling regimes, combining bifurcation theory, experiments, and numerical analysis to reveal the importance of amplitude dynamics.

Findings

Abrupt synchronization transitions occur at strong coupling.

Phase-only models may miss critical features of full system dynamics.

Experimental evidence confirms different transition types.

Abstract

Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling, these transitions can be understood in terms of commonly studied phase approximations. As the coupling strength increases, however, predicting the location and criticality of transition, whether continuous or discontinuous, from the phase dynamics may depend on the order of the phase approximation -- or a phase description of the network dynamics that neglects amplitudes may become impossible altogether. Here we analyze synchronization transitions and their criticality systematically for varying coupling strength in theory and experiments with coupled electrochemical oscillators. First, we analyze bifurcations analysis of synchrony and splay states in an abstract phase model and discuss conditions under which synchronization transitions with different criticalities are possible. Second, we illustrate that transitions with different criticality indeed occur in experimental systems. Third, we highlight that the amplitude dynamics observed in the experiments can be captured in a numerical bifurcation analysis of delay-coupled oscillators. Our results showcase that reduced order phase models may miss important features that one would expect in the dynamics of the full system.