Synchronization Dynamics in the Presence of Coupling Delays and Phase Shifts

TL;DR

This paper explores how time delays and phase shifts influence synchronization in coupled oscillators, revealing that phase shifts can regulate synchronization rates and that intermediate wavelengths optimize synchronization speed in spatial systems.

Contribution

It demonstrates how phase shifts can replace time delays to control synchronization and uncovers optimal wavelengths for fastest synchronization in spatially extended systems.

Findings

Synchronization rates can be tuned by phase shifts.

Fastest synchronization occurs at intermediate wavelengths.

Phase shifts can substitute for time delays at constant frequency.

Abstract

In systems of coupled oscillators, the effects of complex signaling can be captured by time delays and phase shifts. Here, we show how time delays and phase shifts lead to different oscillator dynamics and how synchronization rates can be regulated by substituting time delays by phase shifts at constant collective frequency. For spatially extended systems with time delays, we show that fastest synchronization can occur for intermediate wavelengths, giving rise to novel synchronization scenarios.