{
  "abstract": "We study how network connectivity and heterogeneous phase-delays shape the spatiotemporal dynamics of finite oscillator networks. Phase-delays can destabilize global synchronization and promote phase-locked patterns, including states with uniform phase gradients and more complex combinations of these modes. Yet, how connectivity and phase-delays jointly determine which states the network selects remains unclear. Here, we show that the spectrum of a composite matrix, which combines connectivity and phase-delays, governs not only the linear stability of the network's collective states but also their basin sizes. This, in turn, enables analytical estimates of basin size of phase-locked states for individual networks from connectivity and phase-delays alone. Applying this framework to nonlocal and global networks, including cases with random phase-delays, we uncover multistability and strong asymmetries in basin sizes, revealing chiral dynamics that conventional stability analysis cannot detect.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02047",
  "author_total": 5,
  "authors": [
    {
      "name": "Kalel L. Rossi"
    },
    {
      "name": "Antonio Mihara"
    },
    {
      "name": "Lyle E. Muller"
    },
    {
      "name": "Rene O. Medrano-T"
    },
    {
      "name": "Roberto C. Budzinski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/evm63nk09eecj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02047",
  "fulltext_url": null,
  "id": "evm63nk09eecj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02047",
  "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",
      "math.DS"
    ],
    [
      "arxiv",
      "nlin.AO"
    ],
    [
      "openalex",
      "1705|Nonlinear Dynamics and Pattern Formation"
    ]
  ],
  "openalex": "W7207840796",
  "pdf_url": "https://arxiv.org/pdf/2609.02047",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/evm63nk09eecj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2609.02047",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02047"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.AO",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Phase-delays shape multistability and basin sizes in Kuramoto networks: analytical estimates from network structure",
  "title_text": "Phase-delays shape multistability and basin sizes in Kuramoto networks: analytical estimates from network structure",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/evm63nk09eecj",
  "venue": "arXiv",
  "versions": []
}