Synchronization of two coupled massive oscillators in the time-delayed Kuramoto model

TL;DR

This paper investigates how time delay influences the synchronization and stability of two coupled massive oscillators in the second-order Kuramoto model, revealing multi-stability, non-phase-locked solutions, and chaos.

Contribution

It provides new analytical and numerical insights into the effects of time delay and inertia on oscillator synchronization and stability in the second-order Kuramoto model.

Findings

Time delay induces multi-stability in phase-locked solutions.

Increased inertia reduces the stability of phase-locked states.

Non-phase-locked solutions can be periodic or chaotic depending on parameters.

Abstract

We examine the impact of time delay on two coupled massive oscillators within the second-order Kuramoto model, which is relevant to the operations of real-world networks that rely on signal transmission speed constraints. Our analytical and numerical exploration shows that time delay can cause multi-stability within phase-locked solutions, and the stability of these solutions decreases as inertia increases. In addition to phase-locked solutions, we discovered non-phase-locked solutions that exhibit periodic and chaotic behaviors, depending on the amount of inertia and time delay.