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Benjamin Gess and Michael Scheutzow: Synchronization by noise

Banff International Research Station for Mathematical Innovation and Discovery

We present recent results on synchronization by noise. That is, we introduce su\0cient con- ditions under which weak random attractors for random dynamical systems consist of single random points. These conditions focus on SDE with additive noise, for which they are also essentially necessary. In addition, we provide su\0cient conditions for the existence of a minimal weak point random attractor consisting of a single random point. The analysis passes through the statistical equilibrium, negativity of the top Lyapunov exponent and a local stable manifold result. As a model example, we prove synchronization by noise for an SDE with drift given by a (multidimensional) double-well potential and additive noise. This is joint work with Franco Flandoli.

Mathematics; Dynamical systems and ergodic theory; Probability theory and stochastic processes; Dynamical systems

video/mp4

Author affiliation: University of Chicago

2015-07-22

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/54131

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/