{
  "id": "2012.09003",
  "version": "v1",
  "published": "2020-12-16T14:56:46.000Z",
  "updated": "2020-12-16T14:56:46.000Z",
  "title": "Hopf bifurcation in addition-shattering kinetics",
  "authors": [
    "Stanislav S. Budzinskiy",
    "Sergey A. Matveev",
    "Pavel L. Krapivsky"
  ],
  "comment": "5 pages, 6 figures, 4 pages supplementary, 2 figures supplementary",
  "categories": [
    "cond-mat.stat-mech",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "In aggregation-fragmentation processes, a steady state is usually reached in the long time limit. This indicates the existence of a fixed point in the underlying system of ordinary differential equations. The next simplest possibility is an asymptotically periodic motion. Never-ending oscillations have not been rigorously established so far, although oscillations have been recently numerically detected in a few systems. For a class of addition-shattering processes, we provide convincing numerical evidence for never-ending oscillations in a certain region $\\mathcal{U}$ of the parameter space. The processes which we investigate admit a fixed point that becomes unstable when parameters belong to $\\mathcal{U}$ and never-ending oscillations effectively emerge through a Hopf bifurcation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-16T14:56:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65L12",
      "65L15",
      "G.1.7",
      "G.1.3",
      "I.6.6"
    ],
    "keywords": [
      "hopf bifurcation",
      "addition-shattering kinetics",
      "never-ending oscillations",
      "ordinary differential equations",
      "long time limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}