Stability of anti-bunched buses and local unidirectional Kuramoto oscillators
Abstract
Inspired by our recent work that relates bus bunching as a phenomenon of synchronisation of phase oscillators, we construct a model of Kuramoto oscillators that follows an analogous interaction mechanism of local unidirectional coupling. In the bus loop system, we can introduce a no-boarding policy as a form of kicking force to achieve a stable staggered (anti-bunched) state. For Kuramoto oscillators, it turns out that such stable anti-bunched states can exist (without any additional kicking force) if the number of oscillators are at least five. This correspondence between the bus loop system and the local unidirectional Kuramoto oscillators leads to the insight on how the bus loop system can remain staggered.
Keywords
Cite
@article{arxiv.1912.06470,
title = {Stability of anti-bunched buses and local unidirectional Kuramoto oscillators},
author = {Lock Yue Chew and Vee-Liem Saw and Yi En Ian Pang},
journal= {arXiv preprint arXiv:1912.06470},
year = {2019}
}
Comments
19 pages, 4 figures, 2 videos (https://www.youtube.com/playlist?list=PLZIj25fISvwOALT0PADz_LiH0YbgKMkBz). This work was presented at the 15th International Conference on Dynamical Systems - Theory and Application in {\L}\'od\'z, Poland (2nd to 5th of December, 2019), under the special session dedicated to Prof Miguel A.F. Sanju\'an on the occasion of the celebration of his 60th anniversary