Swarmalators on a ring with distributed couplings

TL;DR

This paper investigates a 1D ring model of swarmalators with distributed couplings, revealing new collective states and generalizing known behaviors, thus bridging simple models and more complex 2D systems.

Contribution

It introduces a 1D ring model with distributed couplings for swarmalators, providing analytical descriptions of new and existing collective states.

Findings

Discovery of new collective states in 1D ring model

Analytical descriptions of swarmalator behaviors

Model captures aspects of 2D swarmalator dynamics

Abstract

We study a simple model of identical swarmalators, generalizations of phases oscillators that swarm through space. We confine the movements to a one-dimensional (1D) ring and consider distributed (non-identical) couplings; the combination of these two effects captures an aspect of the more realistic 2D swarmalator model \cite{o2017oscillators}. We find new collective states as well as generalizations of previously reported ones which we describe analytically. These states imitate the behavior of vinegar eels, catalytic microswimmers, and other swarmalators which move on quasi-1D rings.