{
  "abstract": "Necessary and sufficient conditions are provided for a diffusion-driven instability of a stable equilibrium of a reaction-diffusion system with $n$ components and a diagonal diffusion matrix. These can be either Turing or wave instabilities. Known necessary and sufficient conditions are reproduced for there to exist diffusion rates that cause a Turing bifurcation of a stable homogeneous state in the absence of diffusion. The method of proof here though, which is based on a study of dispersion relations in the contrasting limits in which the wavenumber tends to zero and to $\\infty$, gives a constructive method for choosing diffusion constants. The results are illustrated on a model for the dispersion of malaria, a 3-component FitzHugh-Nagumo-like model proposed to study excitable wavetrains, and for two different coupled Brusselator systems with 4 components",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Villar-Sepúlveda, E., Champneys, A.R. General conditions for Turing and wave instabilities in reaction-diffusion systems. J. Math. Biol. 86, 39 (2023)",
  "arxiv": "2609.28036",
  "author_total": 2,
  "authors": [
    {
      "name": "Edgardo Villar-Sepúlveda"
    },
    {
      "name": "Alan R. Champneys"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/45mh6m1ch9477.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28036",
  "fulltext_url": null,
  "id": "45mh6m1ch9477",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28036",
  "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.PS"
    ]
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.28036",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/45mh6m1ch9477.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.28036",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28036"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.PS",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "General conditions for Turing and wave instabilities in reaction-diffusion systems",
  "title_text": "General conditions for Turing and wave instabilities in reaction-diffusion systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/45mh6m1ch9477",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/s00285-023-01884-x",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}