Dynamics of swarmalators: A pedagogical review

TL;DR

This paper provides a comprehensive review of swarmalators, exploring their collective dynamics, including synchronization and swarming behaviors, through analytical and numerical methods, and discusses future research directions.

Contribution

It offers a systematic pedagogical overview of swarmalator dynamics, highlighting different coupling topologies, interaction functions, and external influences, with insights into long-term behaviors.

Findings

Identification of position aggregation and phase synchronization states

Analysis of effects of coupling topologies and external forcing

Discussion of open problems and future research directions

Abstract

Swarmalators have emerged as a new paradigm for dynamical collective behavior of multi-agent systems due to the interplay of synchronization and swarming that they inherently incorporate. Their dynamics have been explored with different coupling topologies, interaction functions, external forcing, noise, competitive interactions, and from other important viewpoints. Here we take a systematic approach and review the collective dynamics of swarmalators analytically and/or numerically. Long-term states of position aggregation and phase synchronization are revealed in this perspective with some future problems.