Stochastic bifurcations: a perturbative study
| dc.creator | Aumaitre, Sebastien | |
| dc.creator | Mallick, Kirone | |
| dc.creator | Petrelis, Francois | |
| dc.date | 2008-07-28 | |
| dc.date.accessioned | 2026-07-07T09:53:17Z | |
| dc.date.available | 2026-07-07T09:53:17Z | |
| dc.description | We study a noise-induced bifurcation in the vicinity of the threshold by using a perturbative expansion of the order parameter, called the Poincaré-Lindstedt expansion. Each term of this series becomes divergent in the long time limit if the power spectrum of the noise does not vanish at zero frequency. These divergencies have a physical consequence: they modify the scaling of all the moments of the order parameter near the threshold and lead to a multifractal behaviour. We derive this anomalous scaling behaviour analytically by a resummation of the Poincaré-Lindstedt series and show that the usual, deterministic, scalings are recovered when the noise has a low frequency cut-off. Our analysis reconciles apparently contradictory results found in the literature. | |
| dc.identifier | https://arxiv.org/abs/0807.4425 | |
| dc.identifier | http://arxiv.org/abs/0807.4425 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165900 | |
| dc.subject | Chaotic Dynamics | |
| dc.subject | Statistical Mechanics | |
| dc.title | Stochastic bifurcations: a perturbative study | |
| dc.type | text |