{
  "annotation_id": "f490d250-4e95-4258-8e19-c94c43ccd964",
  "date_created": "2026-03-02T18:00:29.174000Z",
  "date_modified": "2026-03-02T18:00:29.174000Z",
  "file_hash": "ecf52ff3bd83be0e1f8520915c963177815b86294ce6c1fe2feef5ffb4ef5823",
  "private": false,
  "record": {
    "abstract": "We re-examine the procedure of adiabatic elimination of fast relaxing\nvariables near a bifurcation point when some of the parameters of the system\nare stochastically modulated. Approximate stationary solutions of the\nFokker-Planck equation are obtained near threshold for the pitchfork and\ntranscritical bifurcations. Stochastic resonance between fast variables and\nrandom modulation may shift the effective bifurcation point by an amount\nproportional to the intensity of the fluctuations. We also find that\nfluctuations of the fast variables above threshold are not always Gaussian and\ncentered around the (deterministic) center manifold as was previously believed.\nNumerical solutions obtained for a few illustrative examples support these\nconclusions.",
    "arxiv_id": "patt-sol/9712001",
    "authors": [
      "Francois Drolet",
      "Jorge Vinals"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevE.57.5036",
    "journal_ref": "Phys. Rev. E 57, 5036 (1998).",
    "title": "Adiabatic reduction near a bifurcation in stochastically modulated   systems",
    "url": "https://arxiv.org/abs/patt-sol/9712001"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "49ed07bc-1ab5-4cf4-b746-91054518001d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}