{
  "id": "1902.08262",
  "version": "v1",
  "published": "2019-02-21T20:55:05.000Z",
  "updated": "2019-02-21T20:55:05.000Z",
  "title": "Stochastic control stabilizing unstable or chaotic maps",
  "authors": [
    "Elena Braverman",
    "Alexandra Rodkina"
  ],
  "comment": "28 pages, 7 figures",
  "doi": "10.1080/10236198.2018.1561882",
  "categories": [
    "math.DS"
  ],
  "abstract": "The paper considers a stabilizing stochastic control which can be applied to a variety of unstable and even chaotic maps. Compared to previous methods introducing control by noise, we relax assumptions on the class of maps, as well as consider a wider range of parameters for the same maps. This approach allows to stabilize unstable and chaotic maps by noise. The interplay between the map properties and the allowed neighbourhood where a solution can start to be stabilized is explored: as instability of the original map increases, the interval of allowed initial conditions narrows. A directed stochastic control aiming at getting to the target neighbourhood almost sure is combined with a controlling noise. Simulations illustrate that for a variety of problems, an appropriate bounded noise can stabilize an unstable positive equilibrium, without a limitation on the initial value.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-21T20:55:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39A50",
      "37H10",
      "93D15",
      "39A30"
    ],
    "keywords": [
      "stochastic control stabilizing unstable",
      "chaotic maps",
      "original map increases",
      "initial conditions narrows",
      "stabilizing stochastic control"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Taylor-Francis"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}