{
  "id": "0901.1283",
  "version": "v1",
  "published": "2009-01-09T17:33:42.000Z",
  "updated": "2009-01-09T17:33:42.000Z",
  "title": "Absolute and Delay-Dependent Stability of Equations with a Distributed Delay: a Bridge from Nonlinear Differential to Difference Equations",
  "authors": [
    "Elena Braverman",
    "Sergey Zhukovskiy"
  ],
  "comment": "23 pages, 4 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant difference equation such that its stability implies stability of the equation with a distributed delay and a finite memory. This result is, generally speaking, incorrect for systems with infinite memory. If the relevant difference equation is unstable, we describe the general delay-independent attracting set and also demonstrate that the equation with a distributed delay is stable for small enough delays.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-09T17:33:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34K20",
      "92D25",
      "34K60",
      "34K23"
    ],
    "keywords": [
      "distributed delay",
      "delay-dependent stability",
      "nonlinear differential",
      "relevant difference equation",
      "study delay-independent stability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}