{
  "annotation_id": "6d8d9c19-e221-4b50-a742-558563c2c416",
  "date_created": "2026-03-02T18:01:21.227000Z",
  "date_modified": "2026-03-02T18:01:21.227000Z",
  "file_hash": "9bb309d6a674e252e5936ed1121572e524b876f449ba0b264a52ffc9f1b5d3be",
  "private": false,
  "record": {
    "abstract": "A general algorithm is presented for estimating the nonlinear instability\nthreshold, $\\sigma_c$, for subcritical transitions in systems where the\nlinearized dynamics is significantly non-normal (i.e. subcritical bifurcations\nof {\\em Takens-Bogdanov} type). The $N$-dimensional degenerate node is\npresented as an example. The predictions are then compared to numerical studies\nwith excellent agreement.",
    "arxiv_id": "physics/9802053",
    "authors": [
      "E. R. Tracy",
      "X. Z. Tang"
    ],
    "categories": [
      "physics.class-ph",
      "math-ph",
      "math.MP",
      "nlin.CD"
    ],
    "doi": "10.1016/S0375-9601(98)00200-X",
    "title": "Anomalous scaling behavior in Takens-Bogdanov bifurcations",
    "url": "https://arxiv.org/abs/physics/9802053"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "77c22149-9a79-430e-8648-69d6a881a604",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}