{
  "id": "1910.06598",
  "version": "v1",
  "published": "2019-10-15T08:55:37.000Z",
  "updated": "2019-10-15T08:55:37.000Z",
  "title": "Global extinction, dissipativity and persistence for a certain class of differential equations with state-dependent delay",
  "authors": [
    "Philipp Getto",
    "Gergely Röst"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we study, at different levels of generality, certain systems of delay differential equations (DDE). One focus and motivation is a system with state-dependent delay (SD-DDE) that has been formulated to describe the maturation of stem cells. We refer to this system as the cell SD-DDE. In the cell SD-DDE, the delay is implicitly defined by a threshold condition. The latter is specified by the time at which the (also implicitly defined) solution of an external nonlinear ordinary differential equation (ODE), which is parametrised by a component of the SD-DDE, meets a given threshold value. We focus on the dynamical properties global asymptotic stability (GAS) of the zero equilibrium, persistence and dissipativity/ultimate boundedness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-15T08:55:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "state-dependent delay",
      "global extinction",
      "persistence",
      "external nonlinear ordinary differential equation",
      "dynamical properties global asymptotic stability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}