{
  "id": "1610.08609",
  "version": "v1",
  "published": "2016-10-27T04:10:29.000Z",
  "updated": "2016-10-27T04:10:29.000Z",
  "title": "Systems of Delay Differential Equations: Analysis of a model with feedback",
  "authors": [
    "Pablo Amster",
    "Carlos Alliera"
  ],
  "comment": "5 pages, 2 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "Self-regulatory models are common in nature, as described e.g. in (\\cite{mur}), (\\cite{ha}) and (\\cite{Gb}).\\\\ Let us consider a system made up of a number of glands as a motivation. Each gland secretes a hormone that allows secretion in the {next} gland, which successively generates another hormone to stimulate the next one and so on. In the end, a final hormone is released which, by increasing its concentration, will inhibit the secretion of previous hormones that allowed the production process. This generates the decay of this hormone to a minimum threshold that re-activates the cycle again.\\\\ This behavior can be seen in other biochemical processes, such as enzymatic or bacterial models.\\\\ Topological degree is a useful tool to find stable equilibria in a wide variety of models with constant parameters and, furthermore, allows to deduce the existence of periodic solutions when the constant parameters are replaced by periodic functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-27T04:10:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34K13"
    ],
    "keywords": [
      "delay differential equations",
      "constant parameters",
      "production process",
      "periodic functions",
      "self-regulatory models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}