{
  "id": "2104.09219",
  "version": "v1",
  "published": "2021-04-19T11:36:10.000Z",
  "updated": "2021-04-19T11:36:10.000Z",
  "title": "Optimal control of a population dynamics model with hysteresis",
  "authors": [
    "Sergey A. Timoshin",
    "Chen Bin"
  ],
  "categories": [
    "math.AP",
    "math.OC"
  ],
  "abstract": "This paper addresses a nonlinear partial differential control system arising in population dynamics. The system consist of three diffusion equations describing the evolutions of three biological species: prey, predator, and food for the prey or vegetation. The equation for the food density incorporates a hysteresis operator of generalized stop type accounting for underlying hysteresis effects occurring in the dynamical process. We study the problem of minimization of a given integral cost functional over solutions of the above system. The set-valued mapping defining the control constraint is state-dependent and its values are nonconvex as is the cost integrand as a function of the control variable. Some relaxation-type results for the minimization problem are obtained and the existence of a nearly optimal solution is established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-19T11:36:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "population dynamics model",
      "optimal control",
      "hysteresis",
      "nonlinear partial differential control system",
      "partial differential control system arising"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}