{
  "abstract": "Swarmalators are mobile generalizations of phase oscillators. Introduced to model systems in which sync and self-assembly interact, they remain poorly understood theoretically. Unlike the Kuramoto model for coupled oscillators, existing swarmalator models lack a normal-form foundation, and their basic stabilities and bifurcations remain largely unsolved. Here we address both problems. Building on Tanaka's reduction of chemotactic oscillators, we show that the canonical one-dimensional swarmalator model -- previously introduced as an ad hoc toy model -- is recovered in the first-harmonic, zero-lag limit, implying its behavior is generic. We then derive the stability boundaries organizing its four collective states, show they meet at a single cusp, correct a previously published order-parameter formula, and uncover a non-monotonic sync response absent in the Kuramoto model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.09810",
  "author_total": 1,
  "authors": [
    {
      "name": "Kevin P. O'Keeffe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a3wmmtmrtnhs2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.09810",
  "fulltext_url": null,
  "id": "a3wmmtmrtnhs2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.09810",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "nlin.AO"
    ],
    [
      "openalex",
      "1705|Nonlinear Dynamics and Pattern Formation"
    ]
  ],
  "openalex": "W7168236698",
  "pdf_url": "https://arxiv.org/pdf/2607.09810",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a3wmmtmrtnhs2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2607.09810",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.09810"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.AO",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "A solvable normal form for coupled swarmalators",
  "title_text": "A solvable normal form for coupled swarmalators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/a3wmmtmrtnhs2",
  "venue": "arXiv",
  "versions": []
}