Transition to complete synchronization in phase coupled oscillators with nearest neighbours coupling

TL;DR

This paper studies how phase-coupled oscillators with nearest neighbor interactions synchronize completely, revealing universal scaling laws and mechanisms for phase locking at the critical coupling point.

Contribution

It introduces a detailed analysis of the transition to complete synchronization, identifying universal scaling behavior and mechanisms for phase locking in a Kuramoto-like model.

Findings

Time intervals between bursts scale universally and diverge at critical coupling.

A key mechanism for phase locking is identified.

Explicit forms for phases and frequencies at synchronization onset are derived.

Abstract

We investigate synchronization in a Kuramoto-like model with nearest neighbour coupling. Upon analyzing the behaviour of individual oscillators at the onset of complete synchronization, we show that the time interval between bursts in the time dependence of the frequencies of the oscillators exhibits universal scaling and blows up at the critical coupling strength. We also bring out a key mechanism that leads to phase locking. Finally, we deduce forms for the phases and frequencies at the onset of complete synchronization.