{
  "abstract": "Early-warning methods can indicate that a system is approaching a loss of stability, but they do not usually reveal whether the approaching bifurcation is supercritical or subcritical. We investigate whether this distinction can be made from noisy pre-transition observations. For this investigation, we extend a regression-based stability method by including the leading cubic nonlinear term, whose sign is used to predict the bifurcation type. We test the method on a stochastic pitchfork model and a spatial stochastic Swift-Hohenberg equation. In both models, classification improves with longer observation horizons, closer proximity to the bifurcation, stronger noise, and larger nonlinear effects. However, these conditions are also linked to a higher risk of noise-induced tipping in the subcritical case. The useful early-warning window is therefore determined by a balance between obtaining enough information to identify the bifurcation type and doing so before noise-induced tipping becomes too likely. In spatially extended systems, we find that observing the full spatial field allows classification over shorter observation horizons, and performance improves when a broader range of spatial modes contributes to the observed dynamics. Altogether, we identify the conditions under which the method can reliably distinguish between supercritical and subcritical bifurcations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38866",
  "author_total": 4,
  "authors": [
    {
      "name": "Paul A. Sanders"
    },
    {
      "name": "Christian Kuehn"
    },
    {
      "name": "Bastian Hilder"
    },
    {
      "name": "Robbin Bastiaansen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/951dg91h9wmqs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38866",
  "fulltext_url": null,
  "id": "951dg91h9wmqs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38866",
  "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.CD"
    ],
    [
      "arxiv",
      "nlin.PS"
    ],
    [
      "arxiv",
      "physics.data-an"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38866",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/951dg91h9wmqs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.38866",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38866"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Early warning of critical transitions: Distinguishing supercritical and subcritical bifurcations from noisy observations",
  "title_text": "Early warning of critical transitions: Distinguishing supercritical and subcritical bifurcations from noisy observations",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/951dg91h9wmqs",
  "venue": "arXiv",
  "versions": []
}