{
  "abstract": "We introduce a novel coupling of Rulkov neural maps, proposing a heuristic biological interpretation for the transition to non-small values of the perturbations acting on the slow variables. We analytically prove that the coupling of two identical neurons preserves the emergence of Devaney chaos through the existence of a generalized snap-back repeller, provided that a snap back repeller exists for the original system. We present numerical simulations for the coupling of two different neurons showing the arising of a potential global strange attractor, whose fractal structure is strongly suggested by the computation of a non-integer Kaplan-Yorke dimension. Furthermore, we perform standard numerical studies concerning time series, Lyapunov exponents spectra, bifurcation diagrams and basins of attraction. Finally, we briefly propose a generalization of the coupling to an arbitrary number of neurons.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.22318",
  "author_total": 1,
  "authors": [
    {
      "name": "Stefano Disca"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9my6xg7xc6x7x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.22318",
  "fulltext_url": null,
  "id": "9my6xg7xc6x7x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.22318",
  "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.CD"
    ],
    [
      "arxiv",
      "q-bio.NC"
    ],
    [
      "openalex",
      "3109|Chaos control and synchronization"
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  ],
  "openalex": "W7171428426",
  "pdf_url": "https://arxiv.org/pdf/2607.22318",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9my6xg7xc6x7x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2607.22318",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.22318"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.NC",
      "subfield": "neuroscience"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "On a cross-coupling of Rulkov neural maps",
  "title_text": "On a cross-coupling of Rulkov neural maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:11Z",
  "url": "https://research.draconitic.com/paper/9my6xg7xc6x7x",
  "venue": "arXiv",
  "versions": []
}