Kevin O'Keeffe, Gourab Kumar Sar, Md Sayeed Anwar, Joao U. F. Lizárraga, Marcus A. M. de Aguiar, Dibakar Ghosh
{"title":"A solvable two-dimensional swarmalator mode","authors":"Kevin O'Keeffe, Gourab Kumar Sar, Md Sayeed Anwar, Joao U. F. Lizárraga, Marcus A. M. de Aguiar, Dibakar Ghosh","doi":"arxiv-2312.10178","DOIUrl":null,"url":null,"abstract":"Swarmalators are oscillators that swarm through space as they synchronize in\ntime. Introduced a few years ago to model many systems which mix synchrony with\nself-assembly, they remain poorly understood theoretically. Here we obtain the\nfirst analytic results on swarmalators moving in two-dimensional (2D) plane by\nenforcing periodic boundary conditions; this simpler topology allows\nexpressions for order parameters, stabilities, and bifurcations to be derived\nexactly. We suggest some future directions for swarmalator research and point\nout some connections to the Kuramoto model and the Vicsek model from active\nmatter; these are intended as a call-to-arms for the sync community and other\nresearchers looking for new problems and puzzles to work on.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"44 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Adaptation and Self-Organizing Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2312.10178","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Swarmalators are oscillators that swarm through space as they synchronize in
time. Introduced a few years ago to model many systems which mix synchrony with
self-assembly, they remain poorly understood theoretically. Here we obtain the
first analytic results on swarmalators moving in two-dimensional (2D) plane by
enforcing periodic boundary conditions; this simpler topology allows
expressions for order parameters, stabilities, and bifurcations to be derived
exactly. We suggest some future directions for swarmalator research and point
out some connections to the Kuramoto model and the Vicsek model from active
matter; these are intended as a call-to-arms for the sync community and other
researchers looking for new problems and puzzles to work on.