{
  "id": "1605.05925",
  "version": "v1",
  "published": "2016-05-19T12:52:42.000Z",
  "updated": "2016-05-19T12:52:42.000Z",
  "title": "Transcritical bifurcation without parameters in memristive circuits",
  "authors": [
    "Ricardo Riaza"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "The transcritical bifurcation without parameters (TBWP) describes a stability change along a line of equilibria, resulting from the loss of normal hyperbolicity at a given point of such a line. Memristive circuits systematically yield manifolds of non-isolated equilibria, and in this paper we address a systematic characterization of the TBWP in circuits with a single memristor. To achieve this we develop two mathematical results of independent interest; the first one is an extension of the TBWP theorem to explicit ordinary differential equations (ODEs) in arbitrary dimension; the second result drives the characterization of this phenomenon to semiexplicit differential-algebraic equations (DAEs), which provide the appropriate framework for the analysis of circuit dynamics. In the circuit context the analysis is performed in graph-theoretic terms: in this setting, our first working scenario is restricted to passive problems (exception made of the bifurcating memristor), and in a second step some results are presented for the analysis of non-passive cases. The latter context is illustrated by means of a memristive neural network model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-19T12:52:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A09",
      "34C45",
      "34D35",
      "37G10",
      "94C05",
      "94C15"
    ],
    "keywords": [
      "transcritical bifurcation",
      "parameters",
      "explicit ordinary differential equations",
      "memristive neural network model",
      "memristive circuits systematically yield manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}