Collective steady-state patterns of swarmalators with finite-cutoff interaction distance

TL;DR

This paper investigates how finite interaction distances affect steady-state patterns in swarmalators, revealing deformation of known patterns and the emergence of new states like bar-like phase waves through numerical and theoretical analysis.

Contribution

It introduces the study of finite-cutoff interaction effects on swarmalator patterns, including the discovery of new static patterns and pattern deformations.

Findings

Infinite-cutoff patterns are reproduced or deformed with finite cutoff.

New bar-like phase wave states are observed at finite cutoff.

Finite cutoff causes shape and density changes in known patterns.

Abstract

We study the steady-state patterns of population of the coupled oscillators that sync and swarm, where the interaction distances among oscillators have finite-cutoff in interaction distance. We examine how the static patterns known in the infinite-cutoff are reproduced or deformed, and explore a new static pattern that does not appear until a finite-cutoff is considered. All steady-state patterns of the infinite-cutoff, static sync, static async, and static phase wave are respectively repeated in space for proper finite-cutoff ranges. Their deformation in shape and density takes place for the other finite-cutoff ranges. Bar-like phase wave states are observed, which has not been the case for the infinite-cutoff. All the patterns are investigated via numerical and theoretical analysis.