{
  "abstract": "We present an analytical organizing principle underlying the dynamics of the periodically forced Duffing oscillator. In the massless limit the system reduces to a time-dependent cubic equation whose discriminant and Jacobian classify the canonical Duffing regimes and determine the number and stability of instantaneous equilibria. For the double-well oscillator, the same construction gives an exact forcing threshold $F_{\\mathrm{bif}}$ separating intra-well and inter-well dynamics. We show that this algebraic quantity governs the finite-mass dynamics far beyond the singular limit from which it originates: the boundary between intra-well and inter-well motion converges to $F_{\\mathrm{bif}}$ as $m\\to0$, and the families of pitchfork bifurcations responsible for asymmetric inter-well states accumulate at a common point. Numerical simulations further show how the discontinuous jumps of the degenerate model are regularized at finite mass into short oscillatory transients that shrink as $m\\to0$. These results reveal the massless Duffing equation as the organizing center of the full finite-mass dynamics and establish a direct link between the algebraic structure of the degenerate problem and the global bifurcation structure of the oscillator.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26719",
  "author_total": 2,
  "authors": [
    {
      "name": "Patrycja Jaros"
    },
    {
      "name": "Przemyslaw Perlikowski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2js2w23b3t0gv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26719",
  "fulltext_url": null,
  "id": "2js2w23b3t0gv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26719",
  "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.CA"
    ],
    [
      "arxiv",
      "nlin.CD"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.26719",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2js2w23b3t0gv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.26719",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26719"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "The cubic discriminant as an organizing principle for Duffing dynamics",
  "title_text": "The cubic discriminant as an organizing principle for Duffing dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/2js2w23b3t0gv",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/hkqh-2824",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}