dorsal/arxiv
View SchemaAnomalous scaling behavior in Takens-Bogdanov bifurcations
| Authors | E. R. Tracy, X. Z. Tang |
|---|---|
| Categories | |
| ArXiv ID | physics/9802053 |
| URL | https://arxiv.org/abs/physics/9802053 |
| DOI | 10.1016/S0375-9601(98)00200-X |
Abstract
A general algorithm is presented for estimating the nonlinear instability threshold, $\sigma_c$, for subcritical transitions in systems where the linearized dynamics is significantly non-normal (i.e. subcritical bifurcations of {\em Takens-Bogdanov} type). The $N$-dimensional degenerate node is presented as an example. The predictions are then compared to numerical studies with excellent agreement.
{
"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
}