{
  "abstract": "We study a nonautonomous compartmental model on the probability simplex for radical vote-share dynamics under delayed policy implementation. The model distinguishes a target regime from an effective regime that adjusts with finite speed and includes a persistent alienation reservoir that can later be mobilised by radical actors. In a symmetric benchmark, persistent alienation destroys the global one-threshold picture: below the local instability threshold, a radical-free centrist--alienated equilibrium may coexist with a stable positive equilibrium, separated by a saddle branch created in a saddle-node bifurcation. By hyperbolic persistence, this coexistence survives near the symmetric baseline, while numerical exploration identifies a wider bistable region under asymmetric perturbations. Delayed implementation further separates target and effective threshold passage, producing a parameter-space lag and an additional state-space lag before a visible response in radical support. The analysis combines a Perron--Frobenius threshold for the frozen radical-free equilibrium, a geometric characterisation of positive equilibria, local adiabatic tracking under slow uniformly subcritical drift, and explicit delay bounds for transversal threshold passage. Under initial matching, the parameter-space delay scales as \\(O(κ_θ^{-1})\\); in a monotone ramp example the bound is nearly attained, whereas the state-space lag is substantially larger and less sensitive to implementation speed. Thus threshold restoration is preventive rather than curative: once the trajectory enters the basin of the radicalised attractor, returning below the local threshold need not restore the radical-free regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Communications in Nonlinear Science and Numerical Simulation 162 (2026), 110392",
  "arxiv": "2608.27742",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander Omelchenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3q975zsyycjr2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27742",
  "fulltext_url": null,
  "id": "3q975zsyycjr2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27742",
  "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.DS"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2608.27742",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3q975zsyycjr2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27742",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27742"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Below-threshold Bistability and Implementation Lag in a Simplex Model of Radical Vote-Share Dynamics",
  "title_text": "Below-threshold Bistability and Implementation Lag in a Simplex Model of Radical Vote-Share Dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/3q975zsyycjr2",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1016/j.cnsns.2026.110392",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}