{
  "abstract": "Early-warning indicators in ecosystems, neural activity, financial markets, and climate systems are often interpreted as evidence that a system is approaching a tipping point, typically understood as a bifurcation at which a previously stable state loses stability or disappears. Such indicators include increased variance, autocorrelation, and dimensional reduction. Here we identify a different mechanism that generates the same statistical signatures without any loss of stability. In stochastic non-normal dynamical systems, asymmetric interactions produce transient amplification that creates episodes of apparent instability despite the persistence of a stable attractor. We refer to these episodes as pseudo-bifurcations. Through analytical results, numerical simulations, and empirical evidence from brain dynamics during epileptic seizures, we show that pseudo-bifurcations reproduce the canonical early-warning signals commonly associated with bifurcation-induced tipping points. Crucially, these signatures arise while the underlying system remains dynamically stable and far from any bifurcation. These results demonstrate that widely used early-warning indicators are not uniquely diagnostic of tipping points. Instead, they may reflect the transient geometry of non-normal dynamics, which are ubiquitous in complex interacting systems. Early-warning indicators such as increased variance, autocorrelation, and dimensional reduction are often interpreted as signs that complex systems in ecology, neuroscience, finance, or climate are approaching a tipping point at which a stable state loses stability or disappears. Here, the authors demonstrate, using brain dynamics during epileptic seizures as an example case, that the same statistical signatures can arise from pseudo-bifurcations in stochastic non-normal systems, showing that these widely used indicators are not uniquely diagnostic of tipping points.",
  "abstract_shown": true,
  "affiliations": [
    "Institute of Risk Analysis, Prediction and Management, Southern University of Science and Technology, Shenzhen, China",
    "Business School, Southern University of Science and Technology, Shenzhen, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Virgile Troude",
      "orcid": "0009-0009-5134-9687"
    },
    {
      "affs": [
        1,
        0
      ],
      "name": "Sandro Claudio Lera",
      "orcid": "0000-0003-4669-4768"
    },
    {
      "affs": [
        0
      ],
      "name": "Ke Wu",
      "orcid": "0000-0002-8118-8011"
    },
    {
      "affs": [
        0
      ],
      "name": "Didier Sornette",
      "orcid": "0000-0001-7874-7962"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5j02j4600wj5n.bib",
  "cited_by": 8,
  "doi": "10.1038/s42005-026-02703-7",
  "fulltext_url": null,
  "id": "5j02j4600wj5n",
  "issns": [
    "2399-3650"
  ],
  "landing_url": "https://doi.org/10.1038/s42005-026-02703-7",
  "language": "en",
  "licence": "CC-BY-NC-ND",
  "licence_label": "CC BY-NC-ND",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2306|Ecosystem dynamics and resilience"
    ]
  ],
  "openalex": "W7163561635",
  "pdf_url": "https://www.nature.com/articles/s42005-026-02703-7_reference.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-04",
  "publisher": "Nature Portfolio",
  "ris": "https://research.draconitic.com/paper/5j02j4600wj5n.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T13:21:18Z",
      "native_id": "W7163561635",
      "source": "openalex",
      "url": "https://doi.org/10.1038/s42005-026-02703-7"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "openalex:2306|Ecosystem dynamics and resilience",
      "subfield": "climate"
    }
  ],
  "title": "Pseudo-bifurcations in stochastic non-normal systems and the limits of early-warning signals",
  "title_text": "Pseudo-bifurcations in stochastic non-normal systems and the limits of early-warning signals",
  "type": "peer-reviewed",
  "updated_at": "2026-11-09T13:21:20Z",
  "url": "https://research.draconitic.com/paper/5j02j4600wj5n",
  "venue": "Communications Physics",
  "versions": []
}