{
  "id": "2211.05755",
  "version": "v1",
  "published": "2022-11-10T18:43:19.000Z",
  "updated": "2022-11-10T18:43:19.000Z",
  "title": "Chemical systems with limit cycles",
  "authors": [
    "Radek Erban",
    "Hye-Won Kang"
  ],
  "categories": [
    "math.DS",
    "q-bio.MN"
  ],
  "abstract": "The dynamics of a chemical reaction network (CRN) is often modelled under the assumption of mass action kinetics by a system of ordinary differential equations (ODEs) with polynomial right-hand sides that describe the time evolution of concentrations of chemical species involved. Given an arbitrarily large integer $K \\in {\\mathbb N}$, we show that there exists a CRN such that its ODE model has at least $K$ stable limit cycles. In particular, we show that $N(K) \\le K+2$, where $N(K)$ is the minimal number of chemical species that a CRN with $K$ limit cycles can have. Bounds on the minimal number of chemical reactions and on the minimal size of CRNs with at most second-order kinetics are also provided for CRNs with $K$ limit cycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-10T18:43:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "limit cycles",
      "chemical systems",
      "minimal number",
      "mass action kinetics",
      "chemical reaction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}