{
  "id": "2309.15241",
  "version": "v1",
  "published": "2023-09-26T20:11:07.000Z",
  "updated": "2023-09-26T20:11:07.000Z",
  "title": "The toric locus of a reaction network is a smooth manifold",
  "authors": [
    "Gheorghe Craciun",
    "Jiaxin Jin",
    "Miruna-Stefana Sorea"
  ],
  "comment": "25 pages, 1 figure",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that the toric locus of a reaction network is a smoothly embedded submanifold of the Euclidean space. More precisely, we prove that the toric locus of a reaction network is the image of an embedding and it is diffeomorphic to the product space between the affine invariant polyhedron of the network and its set of complex-balanced flux vectors. Moreover, we prove that within each affine invariant polyhedron, the complex-balanced equilibrium depends smoothly on the parameters (i.e., reaction rate constants). We also show that the complex-balanced equilibrium depends smoothly on the initial conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-26T20:11:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14P05",
      "14P10",
      "14Q30",
      "34D23",
      "34C08",
      "37E99",
      "92C42"
    ],
    "keywords": [
      "reaction network",
      "toric locus",
      "smooth manifold",
      "affine invariant polyhedron",
      "complex-balanced equilibrium"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}