{
  "abstract": "Coupled logistic maps exhibit collective ordering of their directional phases. As the system parameter varies, the directional phases can undergo a transition from an in-phase state to an anti-phase state, while the individual map trajectories remain chaotic. In this work, we propose a data-driven machine learning (ML) framework based on parameter-aware reservoir computing (PARC) to predict order-parameter dynamics in two representative systems: a logistic map and a two-dimensional coupled map lattice (CML). For the logistic map, the reservoir is trained using only pre-crisis time series data at bifurcation parameter $μ$ values below the attractor-merging crisis ($μ_0 = 3.6786$). The trained reservoir reconstructs the full bifurcation diagram and correctly predicts the transition in the directional order parameter $M(μ)$, from an ordered state ($M \\approx 0$) to a disordered state ($M \\neq 0$) across the crisis point. For the CML, we exploit the spatial homogeneity of the lattice: a single reservoir is trained on the dynamics of one representative lattice site and is then replicated across all $L^2$ sites during prediction, where $L$=50. The replicated reservoir correctly predicts the transition from in-phase synchronization ($θ\\approx 1$) to anti-phase clustered states ($θ\\approx 0$) at $μ\\approx 3.82$, where $θ$ quantifies phase coherence across lattice sites.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00983",
  "author_total": 3,
  "authors": [
    {
      "name": "Shiva Dixit"
    },
    {
      "name": "Swati Chauhan"
    },
    {
      "name": "Manish Dev Shrimali"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/62wg3mjaa9g3q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00983",
  "fulltext_url": null,
  "id": "62wg3mjaa9g3q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00983",
  "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",
      "nlin.CD"
    ],
    [
      "openalex",
      "1702|Neural Networks and Reservoir Computing"
    ]
  ],
  "openalex": "W7206163607",
  "pdf_url": "https://arxiv.org/pdf/2609.00983",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/62wg3mjaa9g3q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "2609.00983",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00983"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Predicting Phase Ordering in Chaotic Maps and Coupled Map Lattices",
  "title_text": "Predicting Phase Ordering in Chaotic Maps and Coupled Map Lattices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:00Z",
  "url": "https://research.draconitic.com/paper/62wg3mjaa9g3q",
  "venue": "arXiv",
  "versions": []
}