{
  "id": "1006.2020",
  "version": "v1",
  "published": "2010-06-10T13:01:33.000Z",
  "updated": "2010-06-10T13:01:33.000Z",
  "title": "Existence and uniqueness of limit cycles in a class of second order ODE's with inseparable mixed terms",
  "authors": [
    "Marco Sabatini"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove a uniqueness result for limit cycles of the second order ODE $\\ddot x + \\dot x \\phi(x,\\dot x) + g(x) = 0$. Under mild additional conditions, we show that such a limit cycle attracts every non-constant solution. As a special case, we prove limit cycle's uniqueness for an ODE studied in \\cite{ETA} as a model of pedestrians' walk. This paper is an extension to equations with a non-linear $g(x)$ of the results presented in \\cite{S}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-10T13:01:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C05"
    ],
    "keywords": [
      "second order ode",
      "inseparable mixed terms",
      "limit cycles uniqueness",
      "limit cycle attracts",
      "mild additional conditions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.chaos.2010.07.002",
      "journal": "Chaos Solitons and Fractals",
      "year": 2010,
      "month": "Dec",
      "volume": 43,
      "number": "1-12",
      "pages": 25
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010CSF....43...25S"
    }
  }
}