Collective behaviour of swarmalators on a 1D ring

TL;DR

This paper investigates the collective dynamics of swarmalators confined to a one-dimensional ring, providing exact solutions for various states and bifurcations, and relating the model to real-world quasi-1D swarmalators.

Contribution

It introduces a solvable 1D ring model for swarmalators, revealing exact collective states and bifurcations, and connects the model to biological systems.

Findings

Exact characterization of collective states and bifurcations.

Identification of behaviors analogous to real-world swarmalators.

Model captures essential features of movement in higher dimensions.

Abstract

We study the collective behavior of swarmalators, generalizations of phase oscillators that both sync and swarm, confined to move on a 1D ring. This simple model captures some of the essence of movement in 2D or 3D but has the benefit of being solvable: most of the collective states and their bifurcations can be specified exactly. The model also captures the behavior of real-world swarmalators which swarm in quasi-1D rings such as bordertaxic sperm and vinegar eels.