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.
@article{arxiv.2406.01208,
title = {Synchronization of two coupled massive oscillators in the time-delayed Kuramoto model},
author = {Esmaeil Mahdavi and Mina Zarei and Farhad Shahbazi},
journal= {arXiv preprint arXiv:2406.01208},
year = {2024}
}