Global synchronization theorem for coupled swarmalators
Adaptation and Self-Organizing Systems
2024-10-24 v1
Abstract
The global stability of oscillator networks has attracted much recent attention. Ordinarily, the oscillators in such studies are motionless; their spatial degrees of freedom are either ignored (e.g. mean field models) or inactive (e.g geometrically embedded networks like lattices). Yet many real-world oscillators are mobile, moving around in space as they synchronize in time. Here we prove a global synchronization theorem for such swarmalators for a simple model where the units' movements are confined to a 1d ring. This can be thought of as a generalization from oscillators connected on random networks to oscillators connected on temporal networks, where the edges are determined by the oscillators' movements.
Cite
@article{arxiv.2410.18011,
title = {Global synchronization theorem for coupled swarmalators},
author = {Kevin P. O'Keeffe},
journal= {arXiv preprint arXiv:2410.18011},
year = {2024}
}