{
  "abstract": "Low-dimensional reduction is crucial for understanding network systems with many units. In a recent advance, Martens and Dharmavaram developed a theory of exact low-dimensional reduction for a general class of mean-field coupled dynamical systems characterized by a mean-field Lie-Scheffers structure. In this paper, we classify mean-field coupled dynamical systems with a mean-field Lie-Scheffers structure, where each unit is described by two real variables. Our classification is based on González-López, Kamran, and Olver's local classification of Lie systems on the plane near generic points and yields 28 types of mean-field coupled dynamical systems. For mean-field coupled systems with units described by two real variables, we first present a general theory on classification and low-dimensional reduction based on the mean-field Lie-Scheffers structure, and then discuss applications to populations of coupled oscillators. We show that low-dimensional reduction is possible for a broad class of populations of limit-cycle oscillators, extending the previously reported reducible class of populations of Stuart-Landau oscillators to include many new models.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28715",
  "author_total": 1,
  "authors": [
    {
      "name": "Kai Tokunaga"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/03sabrz8xxz15.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28715",
  "fulltext_url": null,
  "id": "03sabrz8xxz15",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28715",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "nlin.AO"
    ],
    [
      "openalex",
      "2608|Advanced Differential Equations and Dynamical Systems"
    ]
  ],
  "openalex": "W7223206771",
  "pdf_url": "https://arxiv.org/pdf/2610.28715",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/03sabrz8xxz15.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:18Z",
      "native_id": "2610.28715",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28715"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.AO",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Low-Dimensional Reduction of Mean-Field Coupled Dynamical Systems with Units Described by Two Real Variables: Classification and Applications",
  "title_text": "Low-Dimensional Reduction of Mean-Field Coupled Dynamical Systems with Units Described by Two Real Variables: Classification and Applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/03sabrz8xxz15",
  "venue": "arXiv",
  "versions": []
}