Synchronization of coupled second-order Kuramoto-Sakaguchi oscillators

TL;DR

This paper investigates how inertia and phase shifts influence synchronization in second-order Kuramoto-Sakaguchi oscillators, revealing a transition from discontinuous to continuous synchronization and discovering a new oscillating state.

Contribution

It introduces the effect of inertia as effective phase shifts and identifies a novel oscillating synchronization process in complex networks.

Findings

Inertia converts discontinuous to continuous synchronization transition.

A new oscillating state emerges with increasing coupling strength.

The synchronization phenomena are consistent across various network topologies.

Abstract

We study the synchronization of oscillators with inertias and phase shifts, namely the second-order Kuramoto-Sakaguchi model. Using the self-consistent method, we find that the effect of inertia is the introduction of effective phase shifts. The discontinuous synchronization transition of the Kuramoto-Sakaguchi model changes to a continuous one when the value of inertia is small. In addition, we find a new synchronization process, in which with increasing coupling strength the system reaches an oscillating state instead of complete synchronization due to the cross-effect of phase shifts and inertias. Through numerical simulations, the same type of synchronization process is also found for oscillators in complex networks, including scale-free, small-world and random networks.