{
  "abstract": "We perform an asymptotic analysis of the biased van der Pol equation $\\ddot{x} - ν\\,(1 - x^{2})\\,\\dot{x} + x = a$, where the dissipation parameter is large $(ν\\gg 1)$ and the bias parameter $a$ is a real number between $-1$ and $1$, corresponding to large-amplitude relaxation oscillations along a stable limit cycle. Using an abridged singular perturbation analysis, the period of relaxation oscillations $T(a,ν)$ is obtained that is accurate within $0.1\\%$ of the numerical results for $ν\\gg 1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36398",
  "author_total": 2,
  "authors": [
    {
      "name": "Alain J. Brizard"
    },
    {
      "name": "Desmond L. Carrico"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7pxfh2mt6f94v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36398",
  "fulltext_url": null,
  "id": "7pxfh2mt6f94v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36398",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "physics.class-ph"
    ],
    [
      "openalex",
      "2612|Differential Equations and Numerical Methods"
    ]
  ],
  "openalex": "W7224098038",
  "pdf_url": "https://arxiv.org/pdf/2610.36398",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7pxfh2mt6f94v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.36398",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36398"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.class-ph",
      "subfield": "general"
    }
  ],
  "title": "Asymptotic Analysis of the Biased van der Pol Equation",
  "title_text": "Asymptotic Analysis of the Biased van der Pol Equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/7pxfh2mt6f94v",
  "venue": "arXiv",
  "versions": []
}