{
  "abstract": "Spatial heterogeneity in diffusion is a fundamental feature of excitable media, yet its effect on FitzHugh Nagumo dynamics remains mathematically challenging. We establish stability of solutions with respect to perturbations of the diffusion coefficient, providing a rigorous account of how changes in the medium affect the evolution of the system. Specifically, we prove a continuous dependence result ensuring that small perturbations in diffusion produce small variations in the corresponding solutions. The proof adapts the method of contracting rectangles to variable diffusion, yielding a framework for controlling and comparing solutions associated with different diffusion profiles. This result provides a rigorous link between heterogeneous and homogeneous FitzHugh Nagumo systems and justifies constant-diffusion approximations when the diffusion coefficient is close to a constant. Our analysis advances the understanding of FitzHugh Nagumo dynamics in heterogeneous media by establishing robustness with respect to spatial variations in diffusion.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05770",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander Rodriguez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3kzfj90fjpx82.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05770",
  "fulltext_url": null,
  "id": "3kzfj90fjpx82",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05770",
  "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.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05770",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3kzfj90fjpx82.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05770",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05770"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Continuity and Stability of the FitzHugh Nagumo System with Respect to the Diffusion",
  "title_text": "Continuity and Stability of the FitzHugh Nagumo System with Respect to the Diffusion",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:08Z",
  "url": "https://research.draconitic.com/paper/3kzfj90fjpx82",
  "venue": "arXiv",
  "versions": []
}