{
  "abstract": "We investigate the discrete-time version of the Kuramoto model with phase lag, which comprises globally-coupled phase oscillators of distributed frequencies that are evolving under a nonlinear map. In the continuum limit of an infinite number of oscillators ($N\\to \\infty$), we derive the exact Frobenius-Perron equation for the time evolution of the single-oscillator probability density, and study linear stability of the incoherent state. Instability signals onset of synchronization. The corresponding synchronization threshold is obtained analytically for the case of a Lorentzian distribution of the oscillator frequencies. The threshold differs from that of the continuous-time Kuramoto model, reflecting the fundamentally different stability conditions for discrete-time maps and continuous-time flows. Beyond synchronization threshold, we observe several interesting nonlinear phenomena: Unlike the classical Kuramoto model, the discrete-time version exhibits periodic and chaotic states. Numerical simulations of the finite-$N$ system confirm the analytical prediction for the synchronization threshold, while highlighting breakdown of the celebrated Ott-Antonsen ansatz invoked to conveniently study the continuous-time Kuramoto model in terms of a low-dimensional description.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22715",
  "author_total": 2,
  "authors": [
    {
      "name": "Prashant M. Gade"
    },
    {
      "name": "Shamik Gupta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/70avf27y4fr6w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22715",
  "fulltext_url": null,
  "id": "70avf27y4fr6w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22715",
  "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",
      "1705|Nonlinear Dynamics and Pattern Formation"
    ]
  ],
  "openalex": "W7213996094",
  "pdf_url": "https://arxiv.org/pdf/2609.22715",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/70avf27y4fr6w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.22715",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22715"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Discrete-time Kuramoto model with phase lag: Linear stability analysis and onset of synchronization",
  "title_text": "Discrete-time Kuramoto model with phase lag: Linear stability analysis and onset of synchronization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/70avf27y4fr6w",
  "venue": "arXiv",
  "versions": []
}