{
  "abstract": "In this study, we investigate continuous data assimilation for a class of partly diffusive FitzHugh--Nagumo neural networks with memristive feedback and linear synaptic coupling. The nudging algorithm implemented here only adds a feedback term to the membrane-potential equations, while the recovery and memductance variables remain unobserved. We obtain weighted energy estimates that give sufficient conditions for exponential convergence of the data-assimilated solution to the reference solution under full or coarse membrane potential observations. Moreover, we prove energy-class uniqueness in dimensions one and two. In dimension three, the uniqueness criterion is an \\(L^4\\) membrane-potential initial data. We also establish an observational-noise estimate for locally square-integrable forcing, yielding an asymptotic error bound when the noise energy is eventually bounded.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30480",
  "author_total": 1,
  "authors": [
    {
      "name": "Jing Tian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ab2fxray3xpbs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30480",
  "fulltext_url": null,
  "id": "ab2fxray3xpbs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30480",
  "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",
      "math.AP"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7214575655",
  "pdf_url": "https://arxiv.org/pdf/2609.30480",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ab2fxray3xpbs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:43Z",
      "native_id": "2609.30480",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30480"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Continuous Data Assimilation for Memristive FitzHugh--Nagumo Neural Networks",
  "title_text": "Continuous Data Assimilation for Memristive FitzHugh--Nagumo Neural Networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:43Z",
  "url": "https://research.draconitic.com/paper/ab2fxray3xpbs",
  "venue": "arXiv",
  "versions": []
}