{
  "annotation_id": "e599bdd0-2404-428d-9c96-29a1b9806a37",
  "date_created": "2026-03-02T18:00:29.384000Z",
  "date_modified": "2026-03-02T18:00:29.384000Z",
  "file_hash": "f7e847b269f45e26bdaf44ff0bcb115d785bf36a92c5f14e03c6d32ba46db133",
  "private": false,
  "record": {
    "abstract": "We study the effect of external stochastic modulation on a system with O(2)\nsymmetry that exhibits a Hopf or oscillatory instability in the absence of\nmodulation. The study includes a random component in both the control parameter\nof the bifurcation and in the modulation amplitude. Stability boundaries are\ncomputed by either solving the stationary Fokker-Planck equation in the\nvicinity of the center manifold of the underlying deterministic system whenever\npossible, or by direct numerical solution otherwise. If the modulation\namplitude has a stochastic component, the primary bifurcation is always to\nstanding waves at a value of the control parameter that depends on the\nintensity of the fluctuations. More precisely, and to contrast our results with\nthe case of a deterministic periodic forcing, the onset of instability in the\nstanding wave regime is shifted from its deterministic location, and the region\nof primary bifurcation to traveling waves disappears yielding instead standing\nwaves at negative values of the control parameter.",
    "arxiv_id": "patt-sol/9704005",
    "authors": [
      "Francois Drolet",
      "Jorge Vinals"
    ],
    "categories": [
      "patt-sol",
      "cond-mat",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevE.56.2649",
    "journal_ref": "Phys. Rev. E 56, 2649 (1997).",
    "title": "Onset of oscillatory instabilities under stochastic modulation",
    "url": "https://arxiv.org/abs/patt-sol/9704005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d4a9fdd1-90ac-49db-849a-8a107db37180",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}