{
  "abstract": "Two-stage contagion describes processes, such as the adoption of an opinion or of a technological novelty, in which an individual must be exposed to an adopter twice before adopting. With demographic turnover these processes can generate waves of adoption and abandonment. We study these oscillations in a two-stage contagion model with turnover through a reservoir of inactive individuals and a small rate of spontaneous activation, and report four main findings. (i) In the mean-field description the oscillations are born at a supercritical Hopf bifurcation and require a predominantly two-stage contagion (first-contact adoption probability $Q\\lesssim0.17$) and a slow turnover; spontaneous activation acts as a perturbation that destroys them. (ii) In finite populations demographic noise sustains quasi-cycles also outside this region, with a spectrum and variance predicted by a linear noise approximation away from the Hopf bifurcation. (iii) Reducing the connectivity of the network damps the oscillation, because naive nodes see fewer active neighbours than in a well-mixed population, and correlations measured in simulations confirm this damping mechanism; a pair approximation predicts that the sustained cycle disappears below a critical mean degree $\\kc$, which decreases as $Q$ and the turnover rate decrease, and a finite-size test with up to $3.2\\times10^5$ nodes confirms this threshold in simulations. (iv) At low connectivity the amplitude no longer depends on $Q$, so that sparsity erases the signature of the two-stage mechanism, whereas a faster turnover reduces the relative amplitude at every connectivity. The irregular dynamics observed in simulations are noise-driven quasi-cycles, not chaos.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.12920",
  "author_total": 4,
  "authors": [
    {
      "name": "Francisco J. Muñoz"
    },
    {
      "name": "Juan Carlos Nuño"
    },
    {
      "name": "Luca Meacci"
    },
    {
      "name": "Mario Primicerio"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dcamdmg0yespx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.12920",
  "fulltext_url": null,
  "id": "dcamdmg0yespx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.12920",
  "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"
    ],
    [
      "arxiv",
      "nlin.AO"
    ],
    [
      "arxiv",
      "physics.soc-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.12920",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dcamdmg0yespx.ris",
  "sources": [
    {
      "first_seen": "2026-11-11T06:21:45Z",
      "native_id": "2611.12920",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.12920"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.AO",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Oscillations in two-stage contagion on networks: contagion structure, turnover and connectivity",
  "title_text": "Oscillations in two-stage contagion on networks: contagion structure, turnover and connectivity",
  "type": "preprint",
  "updated_at": "2026-11-13T06:20:11Z",
  "url": "https://research.draconitic.com/paper/dcamdmg0yespx",
  "venue": "arXiv",
  "versions": []
}