{
  "id": "1904.12842",
  "version": "v1",
  "published": "2019-04-29T17:49:11.000Z",
  "updated": "2019-04-29T17:49:11.000Z",
  "title": "On stability of delay equations with positive and negative coefficients with applications",
  "authors": [
    "Leonid Berezansky",
    "Elena Braverman"
  ],
  "comment": "33 pages, 3 figures",
  "journal": "Zeitschrift f\\\"{u}r Analysis und ihre Anwendungen, Volume 38, Issue 2, 2019, 157-189",
  "categories": [
    "math.DS"
  ],
  "abstract": "We obtain new explicit exponential stability conditions for linear scalar equations with positive and negative delayed terms $$ \\dot{x}(t)+ \\sum_{k=1}^m a_k(t)x(h_k(t))- \\sum_{k=1}^l b_k(t)x(g_k(t))=0 $$ and its modifications, and apply them to investigate local stability of Mackey--Glass type models $$\\dot{x}(t)=r(t)\\left[\\beta\\frac{x(g(t))}{1+x^n(g(t))}-\\gamma x(h(t))\\right]$$ and $$\\dot{x}(t)=r(t)\\left[\\beta\\frac{x(g(t))}{1+x^n(h(t))}-\\gamma x(t)\\right].$$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-29T17:49:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34K20",
      "34K06",
      "92D25"
    ],
    "keywords": [
      "delay equations",
      "negative coefficients",
      "applications",
      "explicit exponential stability conditions",
      "mackey-glass type models"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}