Attractive and repulsive interactions in the one-dimensional swarmalator model

TL;DR

This paper investigates a 1D swarmalator model with attractive and repulsive interactions, revealing various collective states including synchronized, asynchronous, polarized, and unsteady behaviors, with some states analytically described.

Contribution

It introduces a simple 1D swarmalator model that captures multiple collective states and provides analytical descriptions for some of these states.

Findings

Identification of multiple collective states including sync, async, polarized, and unsteady.

Analytical descriptions for certain states within the model.

Potential relevance to real-world quasi-1D swarmalators like vinegar eels.

Abstract

We study a population of swarmalators, mobile variants of phase oscillators, which run on a ring and have both attractive and repulsive interactions. This one-dimensional (1D) swarmalator model produces several of collective states: the standard sync and async states as well as a splaylike "polarized" state and several unsteady states such as active bands or swirling. The model's simplicity allows us to describe some of the states analytically. The model can be considered as a toy model for real-world swarmalators such as vinegar eels and sperm which swarm in quasi-1D geometries.