{
  "annotation_id": "826f6947-1527-4cc2-bd5c-75993c4c479a",
  "date_created": "2026-03-02T18:00:39.115000Z",
  "date_modified": "2026-03-02T18:00:39.115000Z",
  "file_hash": "d253c3cb7762882a80d6d3ba0d0330b4a5e5ad56466758e5d789e43c8f3f0d1b",
  "private": false,
  "record": {
    "abstract": "The random map model is a deterministic dynamical system in a finite phase\nspace with n points. The map that establishes the dynamics of the system is\nconstructed by randomly choosing, for every point, another one as being its\nimage. We derive here explicit formulas for the statistical distribution of the\nnumber of attractors in the system. As in related results, the number of\noperations involved by our formulas increases exponentially with n; therefore,\nthey are not directly applicable to study the behavior of systems where n is\nlarge. However, our formulas lend themselves to derive useful asymptotic\nexpressions, as we show.",
    "arxiv_id": "physics/0207044",
    "authors": [
      "David Romero",
      "Federico Zertuche"
    ],
    "categories": [
      "physics.bio-ph",
      "physics.gen-ph"
    ],
    "doi": "10.1088/0305-4470/36/13/304",
    "title": "The Asymptotic Number of Attractors in the Random Map Model",
    "url": "https://arxiv.org/abs/physics/0207044"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b9803281-4cd0-44a5-8115-0ce466e0cfda",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}