{
  "id": "2310.19604",
  "version": "v2",
  "published": "2023-10-30T14:58:15.000Z",
  "updated": "2024-08-28T02:16:21.000Z",
  "title": "Hybrid Bifurcations: Periodicity from Eliminating a Line of Equilibria",
  "authors": [
    "Alejandro López-Nieto",
    "Phillipo Lappicy",
    "Nicola Vassena",
    "Hannes Stuke",
    "Jia-Yuan Dai"
  ],
  "comment": "Change of title from v1, typos corrected",
  "categories": [
    "math.DS",
    "math.CA"
  ],
  "abstract": "We describe a new mechanism that triggers periodic orbits in smooth dynamical systems. To this end, we introduce the concept of hybrid bifurcations: Such bifurcations occur when a line of equilibria with an exchange point of normal stability vanishes. Our main result is the existence and stability criteria of periodic orbits that bifurcate from breaking a line of equilibria. As an application, we obtain stable periodic coexistent solutions in an ecosystem for two competing predators with Holling's type II functional response.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-08-28T02:16:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C20",
      "34C25",
      "34D20",
      "37G10",
      "37J40",
      "92D25"
    ],
    "keywords": [
      "hybrid bifurcations",
      "equilibria",
      "periodicity",
      "triggers periodic orbits",
      "stable periodic coexistent solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}