{
  "id": "1309.6771",
  "version": "v4",
  "published": "2013-09-26T09:30:45.000Z",
  "updated": "2014-08-26T09:30:33.000Z",
  "title": "Some results on injectivity and multistationarity in chemical reaction networks",
  "authors": [
    "Murad Banaji",
    "Casian Pantea"
  ],
  "comment": "considerably revised and corrected; some new results added",
  "categories": [
    "math.DS"
  ],
  "abstract": "The goal of this paper is to gather and develop some necessary and sufficient criteria for injectivity and multistationarity in vector fields associated with a chemical reaction network under a variety of more or less general assumptions on the nature of the network and the reaction rates. The results are primarily linear algebraic or matrix-theoretic, with some graph-theoretic corollaries also mentioned. Where possible, elementary proofs are presented, and a number of examples are provided to illustrate the variety of subtly different conclusions which can be reached via different computations. In addition, many of the computations are implemented in a web-based open source platform, allowing the reader to test examples including and beyond those analysed in the paper.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-01-21T11:25:05.000Z",
      "abstract": "The goal of this paper is to gather and develop some necessary and sufficient criteria for injectivity and multistationarity of vector fields associated with a chemical reaction network under a variety of more or less general assumptions on the nature of the network and the reaction rates. The results are primarily linear algebraic or matrix-theoretic, with some graph-theoretic corollaries also mentioned. Where possible, elementary proofs are presented, and a number of examples are provided to illustrate the variety of subtly different conclusions which can be reached via different computations. In addition, many of the computations are implemented in a web-based open source platform, allowing the reader to test examples including and beyond those analysed in the paper.",
      "comment": "some errors corrected, examples and remarks added",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-08-26T09:30:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "80A30",
      "15A15",
      "37C25"
    ],
    "keywords": [
      "chemical reaction network",
      "injectivity",
      "multistationarity",
      "web-based open source platform",
      "sufficient criteria"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.6771B"
    }
  }
}