Stochastic bifurcations: a perturbative study

Details Stochastic bifurcations: a perturbative study Stochastic bifurcations: a perturbative study

2008-07-28

arxiv.org/abs/0807.4425v1

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

We study a noise-induced bifurcation in the vicinity of the threshold by using a perturbative expansion of the order parameter, called the Poincar\'e-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 Poincar\'e-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.

Affiliated with

Also associated with

No associations

Rating

Stochastic bifurcations: a perturbative study does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Stochastic bifurcations: a perturbative study, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stochastic bifurcations: a perturbative study will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-313036