{
  "abstract": "We construct a seven-cycle example for a periodically forced scalar equation with a continuous three-zone piecewise-linear nonlinearity. Symbolic integration and linear elimination reduce the four-flight matching conditions to two equations in the residence times. The competing exterior visits produce an additional turn of the critical response and lead to the rational parameters $(A,B,μ)=(9,3/2,181363/100000)$. At these parameters, finite Taylor estimates give three sign changes of the return displacement. Scalar order, analyticity along transverse itineraries, and half-period reflection then establish at least seven distinct isolated periodic orbits on the phase cylinder.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19586",
  "author_total": 2,
  "authors": [
    {
      "name": "Chaoyu Hu"
    },
    {
      "name": "Jizheng Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e90z83hwsn2gp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19586",
  "fulltext_url": null,
  "id": "e90z83hwsn2gp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19586",
  "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",
      "cs.SC"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "nlin.CD"
    ],
    [
      "openalex",
      "2608|Advanced Differential Equations and Dynamical Systems"
    ]
  ],
  "openalex": "W7222341629",
  "pdf_url": "https://arxiv.org/pdf/2610.19586",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e90z83hwsn2gp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.19586",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19586"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Seven Limit Cycles in a Periodically Forced Three-Zone Equation",
  "title_text": "Seven Limit Cycles in a Periodically Forced Three-Zone Equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/e90z83hwsn2gp",
  "venue": "arXiv",
  "versions": []
}