{
  "id": "1607.01080",
  "version": "v1",
  "published": "2016-07-05T00:27:17.000Z",
  "updated": "2016-07-05T00:27:17.000Z",
  "title": "Algorithm for rigorous integration of Delay Differential Equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation",
  "authors": [
    "Robert Szczelina",
    "Piotr Zgliczyński"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We present an algorithm for the rigorous integration of Delay Differential Equations (DDEs) of the form $x'(t)=f(x(t-\\tau),x(t))$. As an application we give a computer assisted proof of the existence of two attracting periodic orbits (before and after the first period-doubling bifurcation) in the Mackey-Glass equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-05T00:27:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34K13",
      "65G30",
      "65Q20",
      "G.1.0",
      "G.1.9"
    ],
    "keywords": [
      "delay differential equations",
      "mackey-glass equation",
      "rigorous integration",
      "computer-assisted proof",
      "computer assisted proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}