Additive noise destroys the random attractor close to bifurcation
Dynamical Systems
2017-11-20 v1 Probability
Abstract
We provide an example for stabilization by noise. Our approach does not rely on monotonicity arguments due to the presence of higher order differential operators or mixing properties of the system as the noise might be highly degenerate. In the examples a scalar additive noise destroys a high-dimensional random attractor of a PDE on an unbounded domain. In the presence of small noise close to bifurcation all trajectories converge to a single stationary solution.
Keywords
Cite
@article{arxiv.1603.05500,
title = {Additive noise destroys the random attractor close to bifurcation},
author = {Luigi Amedeo Bianchi and Dirk Blömker and Meihua Yang},
journal= {arXiv preprint arXiv:1603.05500},
year = {2017}
}