Synchronization by noise
Abstract
We provide sufficient conditions for synchronization by noise, i.e. under these conditions we prove that weak random attractors for random dynamical systems consist of single random points. In the case of SDE with additive noise, these conditions are also essentially necessary. In addition, we provide sufficient conditions for the existence of a minimal weak point random attractor consisting of a single random point. As a result, synchronization by noise is proven for a large class of SDE with additive noise. In particular, we prove that the random attractor for an SDE with drift given by a (multidimensional) doublewell potential and additive noise consists of a single random point. All examples treated in [Tearne, PTRF; 2008] are also included.
 Publication:

arXiv eprints
 Pub Date:
 November 2014
 arXiv:
 arXiv:1411.1340
 Bibcode:
 2014arXiv1411.1340F
 Keywords:

 Mathematics  Probability;
 Mathematics  Dynamical Systems;
 37B25;
 37G35;
 37H15
 EPrint:
 45 pages