{
  "abstract": "Stochastic forcing can prevent diversity collapse in competitive dynamical systems, yet the quantitative conditions and the dynamical mechanism responsible remain poorly characterized. We address both questions in a class of nonlinear stochastic replicator dynamics on the N-dimensional probability simplex, parameterized by a nonlinearity exponent gamma and additive Gaussian noise of intensity sigma. Under the baseline interaction, the minimum noise required to sustain diversity decays as a power law, sigma_c ~ N^(-alpha); replacing the baseline interaction with a superlinear variant shifts alpha from about 1.1 to about 2.0, in agreement with a linear-stability prediction alpha = (gamma+2)/2, identifying alpha as a model-specific quantity rather than a universal index. Scanning the (gamma, sigma) plane reveals a smooth dynamical crossover: the fluctuation susceptibility chi_H = N Var(H) peaks at gamma ~ 0.7 (chi_H ~ 0.6) and is suppressed at high gamma, with no divergence near gamma ~ 1.4; matched finite-size analysis finds no systematic divergence of the peak with N, ruling out a genuine second-order phase transition. The entropy relaxation time tau_relax(gamma) remains approximately constant (about 2.9 time units) across the full range of gamma, even as chi_H decreases sixfold; this decoupling between relaxation timescale and fluctuation amplitude implies that suppression arises from convergence of diverse pathways to similar endpoints rather than from accelerated relaxation along a single channel. These findings identify nonlinear fluctuation suppression via pathway multiplicity -- distinct from both noise-induced transitions and equilibrium criticality -- as the operative stabilization pattern in this class of nonequilibrium stochastic systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Physica A 701 (2026) 132041",
  "arxiv": "2610.30169",
  "author_total": 1,
  "authors": [
    {
      "name": "Ruocun Ou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3xc74nqnt2t3v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30169",
  "fulltext_url": null,
  "id": "3xc74nqnt2t3v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30169",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "nlin.AO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.30169",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3xc74nqnt2t3v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.30169",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30169"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Stochastic Diversity Stabilization in Nonlinear Competitive Dynamics: A Statistical Mechanics Approach to Fluctuation Suppression and Finite-Size Scaling",
  "title_text": "Stochastic Diversity Stabilization in Nonlinear Competitive Dynamics: A Statistical Mechanics Approach to Fluctuation Suppression and Finite-Size Scaling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:34Z",
  "url": "https://research.draconitic.com/paper/3xc74nqnt2t3v",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1016/j.physa.2026.132041",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}