{
  "abstract": "General expressions are derived for the amplitude equation valid at a Turing bifurcation of a system of reaction-diffusion equations in one spatial dimension, with an arbitrary number of components. The normal form is computed up to fifth order, which enables the detection and analysis of codimension-two points where the criticality of the bifurcation changes. The expressions are implemented within a Python package, in which the user needs to specify only expressions for the reaction kinetics and the values of diffusion constants. The code is augmented with a Mathematica routine to compute curves of Turing bifurcations in a parameter plane and automatically detect codimension-two points. The software is illustrated with examples that show the versatility of the method including a case with cross-diffusion, a higher-order scalar equation, and a four-component system.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Edgardo Villar-Sepúlveda and Alan Champneys. 2023. Computation of Turing Bifurcation Normal Form for n-Component Reaction-Diffusion Systems. ACM Trans. Math. Softw. 49, 4, Article 35 (December 2023)",
  "arxiv": "2609.28039",
  "author_total": 2,
  "authors": [
    {
      "name": "Edgardo Villar-Sepúlveda"
    },
    {
      "name": "Alan R. Champneys"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3aa5fq13pm2fr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28039",
  "fulltext_url": null,
  "id": "3aa5fq13pm2fr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28039",
  "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": [
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      "arxiv",
      "nlin.PS"
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.28039",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3aa5fq13pm2fr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.28039",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28039"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.PS",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Computation of Turing bifurcation normal form for n-component reaction-diffusion systems",
  "title_text": "Computation of Turing bifurcation normal form for n-component reaction-diffusion systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/3aa5fq13pm2fr",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1145/3625560",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
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}