{
  "id": "1504.03353",
  "version": "v1",
  "published": "2015-04-13T20:31:39.000Z",
  "updated": "2015-04-13T20:31:39.000Z",
  "title": "Global bifurcations of limit cycles in a Holling-type dynamical system",
  "authors": [
    "Valery A. Gaiko"
  ],
  "comment": "19 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1104.3019, arXiv:0902.2433",
  "categories": [
    "math.DS",
    "math.CA"
  ],
  "abstract": "In this paper, we complete the global qualitative analysis of a quartic family of planar vector fields corresponding to a rational Holling-type dynamical system which models the dynamics of the populations of predators and their prey in a given ecological or biomedical system. In particular, studying global bifurcations, we prove that such a system can have at most two limit cycles surrounding one singular point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-13T20:31:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C05",
      "34C07",
      "37G10",
      "37G15",
      "92D25"
    ],
    "keywords": [
      "limit cycles",
      "rational holling-type dynamical system",
      "global qualitative analysis",
      "planar vector fields corresponding",
      "singular point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150403353G"
    }
  }
}