{
  "abstract": "In this paper, we study a slow-fast model of Intracellular Calcium Concentrations (ICC) within a stochastic framework, where stochastic perturbations are introduced to capture the intrinsic randomness of such biological systems. We first analyse the three-dimensional single-cell model, based on the FitzHugh-Nagumo structure, and subsequently extend the analysis to a coupled two-cell six-dimensional setting. We prove existence and uniqueness of solutions and establish positivity of the calcium variable. We obtain explicit mean-square stability estimates around deterministic equilibria and quantify how they depend on the noise intensity. Numerical simulations for both the single-cell and coupled systems illustrate relevant qualitative behaviours and reveal additional dynamical features arising in the stochastic framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13213",
  "author_total": 3,
  "authors": [
    {
      "name": "Tomás Caraballo"
    },
    {
      "name": "Macarena Gómez-Mármol"
    },
    {
      "name": "Ignacio Roldán"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4sw6xj2t0q7bz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13213",
  "fulltext_url": null,
  "id": "4sw6xj2t0q7bz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13213",
  "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.DS"
    ],
    [
      "arxiv",
      "q-bio.CB"
    ],
    [
      "openalex",
      "3109|stochastic dynamics and bifurcation"
    ]
  ],
  "openalex": "W7213224035",
  "pdf_url": "https://arxiv.org/pdf/2609.13213",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4sw6xj2t0q7bz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13213",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13213"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.CB",
      "subfield": "cell-biology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "A Stochastic Model of Intracellular Calcium Concentrations",
  "title_text": "A Stochastic Model of Intracellular Calcium Concentrations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:30Z",
  "url": "https://research.draconitic.com/paper/4sw6xj2t0q7bz",
  "venue": "arXiv",
  "versions": []
}