Synchronization of the time-delayed Kuramoto model in a regular network

TL;DR

This paper explores how time delays affect synchronization in a ring of identical oscillators using the Kuramoto model, revealing various dynamic regimes and the emergence of moving-turbulent Chimera states.

Contribution

It provides a combined analytical and numerical analysis of delay-induced synchronization phenomena and identifies conditions for different collective behaviors in the Kuramoto model.

Findings

Delay can inhibit or promote synchronization depending on the regime.

Multiple dynamic states including fully synchronized, helical, and Chimera states are observed.

Moving-turbulent Chimera states are identified in certain delay regimes.

Abstract

This study investigates the impact of delayed coupling on the global and local synchronization of identical coupled oscillators residing in a ring. Utilizing the Kuramoto model, we examine the effects of delayed coupling on collective dynamics. Our analytical and numerical results reveal distinct synchronization behaviors across various time delay regimes, including fully synchronized states, helical patterns, dynamically incoherent states, and random phase-locked states. We identify the regime in which time delay inhibits synchrony, which aligns with theoretical predictions derived from stability analysis. In the region between the synchrony-possible and synchrony-forbidden zones, a coexistence of synchronized and unsynchronized dynamics is observed, referred to as Chimera states. We ascertain that the type of Chimera states present is moving-turbulent.