{
  "abstract": "We study extinction and extinguishment in a two-type continuous-state nonlinear branching model driven by Brownian branching noise and spectrally positive stable jumps. The populations are subject to nonlinear self-regulation and a mixed-sign predator--prey interaction: the second promotes the first, whereas the first suppresses the second. Two complementary structures are developed. An exact power--logarithmic cancellation functional removes the interaction drifts and yields stochastic Lyapunov estimates, nonexplosion, and boundary criteria. In the multiplicative regimes, integrating-factor identities and geometric Lévy factorizations express extinction through weighted exposure clocks and reduce the long-time analysis to effective decay rates. These methods yield almost-sure extinction criteria and identify a regime in which finite-time extinction and nonextinction coexist. On nonextinction, both populations remain positive at all finite times and converge jointly to zero, exhibiting joint extinguishment rather than positive persistence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30178",
  "author_total": 4,
  "authors": [
    {
      "name": "Lina Ji"
    },
    {
      "name": "Jie Xiong"
    },
    {
      "name": "Wen Xu"
    },
    {
      "name": "Xu Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8bcw9wsq5x4rp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30178",
  "fulltext_url": null,
  "id": "8bcw9wsq5x4rp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30178",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7204928514",
  "pdf_url": "https://arxiv.org/pdf/2608.30178",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8bcw9wsq5x4rp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30178",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30178"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Extinction and extinguishment properties for a nonlinear predator-prey branching model",
  "title_text": "Extinction and extinguishment properties for a nonlinear predator-prey branching model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/8bcw9wsq5x4rp",
  "venue": "arXiv",
  "versions": []
}