{
  "abstract": "We study cooperative nonlocal transport on a circle with species-dependent constant velocities and arbitrary $L^1$ probability kernels. For periodic coefficients, the period map is a compact perturbation of the no-jump map. We construct separate receiving and sending characteristic scans: under a two-tree condition based at one active component, a positive Floquet profile exists exactly when the full period map has strictly larger spectral radius than its no-jump part. The other jump rates may vanish. The scans provide an integral minorant and positive jump return; a separate coefficient inequality verifies the spectral gap. Smooth locking examples distinguish communication from frozen-time mixing, while a resonant example separates positive return from spectral separation. Autonomous nonzero velocities and union-graph connectivity yield a simple principal pair; one active component suffices for exponential mixing. We also prove local perturbation results. For quadratic self-regulation, the same principal projection gives a transverse response whose averaged cubic coefficient is a nonnegative asymptotic variance. It determines both the critical $t^{-2}\\log t$ correction and the second-order period-averaged amplitude of the positive branch.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36851",
  "author_total": 1,
  "authors": [
    {
      "name": "Bing He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6n4b47j3vy2hc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36851",
  "fulltext_url": null,
  "id": "6n4b47j3vy2hc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36851",
  "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.AP"
    ],
    [
      "openalex",
      "2739|Mathematical and Theoretical Epidemiology and Ecology Models"
    ]
  ],
  "openalex": "W7224105287",
  "pdf_url": "https://arxiv.org/pdf/2610.36851",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6n4b47j3vy2hc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36851",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36851"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Principal profiles, characteristic communication and critical asymptotics for cooperative nonlocal systems on the circle",
  "title_text": "Principal profiles, characteristic communication and critical asymptotics for cooperative nonlocal systems on the circle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/6n4b47j3vy2hc",
  "venue": "arXiv",
  "versions": []
}