{
  "abstract": "We investigate differential equations defined through elements of a nonassociative five-dimensional real algebra $\\mathcal A_γ$, and show that every system of quadratic differential equations $\\dot p=F(p)$ on $\\mathbb R^5$ can be written as a differential equation over such a non-flexible quadratic algebra. We then study quadratic differential equations and their solutions over the whole family $\\{\\mathcal A_γ\\}_{0\\leqγ\\leq1}$ of algebras while varying $γ$ across the parameter interval $[0,1]$, exploiting the fact that by definition, $\\mathcal A_0$ contains Hamilton's quaternion algebra and that $\\mathcal A_1=\\mathbb{P}$ is the real Pentarnion algebra. We construct explicit Jacobi elliptic solutions that deform a quaternion-valued solution at $γ=0$ into a Pentarnion-valued one at $γ=1$, and an algebra-valued Riccati equation whose equilibrium $p=0$ loses stability at a critical value of $γ$. Numerical experiments indicate period doubling, coexisting stable periodic orbits and irregular dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34201",
  "author_total": 2,
  "authors": [
    {
      "name": "Alireza Poshtkohi"
    },
    {
      "name": "Susanne Pumpluen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d8pf6bfgsqnpx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34201",
  "fulltext_url": null,
  "id": "d8pf6bfgsqnpx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34201",
  "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",
      "math.RA"
    ],
    [
      "openalex",
      "2604|Algebraic and Geometric Analysis"
    ]
  ],
  "openalex": "W7223912437",
  "pdf_url": "https://arxiv.org/pdf/2610.34201",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d8pf6bfgsqnpx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34201",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34201"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "From Quaternions to Pentarnions II: quadratic differential equations",
  "title_text": "From Quaternions to Pentarnions II: quadratic differential equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/d8pf6bfgsqnpx",
  "venue": "arXiv",
  "versions": []
}