When time delays and phase lags are not the same: higher-order phase reduction unravels delay-induced synchronization in oscillator networks

TL;DR

This paper introduces a systematic method for higher-order phase reduction of delay-coupled oscillators, enabling accurate analysis of delay-dependent synchronization phenomena that first-order reductions fail to capture.

Contribution

The authors develop a systematic approach for deriving higher-order phase reductions in delay-coupled oscillators, improving the prediction of delay-dependent synchronization stability.

Findings

Second-order reduction predicts delay-dependent stability.

Method applied successfully to Stuart-Landau oscillators.

Higher-order reductions capture complex delay effects.

Abstract

Coupled oscillators with time-delayed network interactions are critical to understand synchronization phenomena in many physical systems. Phase reductions to finite-dimensional phase oscillator networks allow for their explicit analysis. However, first-order phase reductions - where delays correspond to phase lags - fail to capture the delay-dependence of synchronization. We develop a systematic approach to derive phase reductions for delay-coupled oscillators to arbitrary order. Already the second-order reduction can predict delay-dependent (bi-)stability of synchronized states as demonstrated for Stuart-Landau oscillators.