dorsal/arxiv
View SchemaOnset of oscillatory instabilities under stochastic modulation
| Authors | Francois Drolet, Jorge Vinals |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9704005 |
| URL | https://arxiv.org/abs/patt-sol/9704005 |
| DOI | 10.1103/PhysRevE.56.2649 |
| Journal | Phys. Rev. E 56, 2649 (1997). |
Abstract
We study the effect of external stochastic modulation on a system with O(2) symmetry that exhibits a Hopf or oscillatory instability in the absence of modulation. The study includes a random component in both the control parameter of the bifurcation and in the modulation amplitude. Stability boundaries are computed by either solving the stationary Fokker-Planck equation in the vicinity of the center manifold of the underlying deterministic system whenever possible, or by direct numerical solution otherwise. If the modulation amplitude has a stochastic component, the primary bifurcation is always to standing waves at a value of the control parameter that depends on the intensity of the fluctuations. More precisely, and to contrast our results with the case of a deterministic periodic forcing, the onset of instability in the standing wave regime is shifted from its deterministic location, and the region of primary bifurcation to traveling waves disappears yielding instead standing waves at negative values of the control parameter.
{
"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
}