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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium

Jonathan Mattingly
Duke University
Title: Stabilization by noise

Abstract: Noise is usually though of as a destabilizing force. I will discuss a few examples where the noise has a stabilizing effect. I will begin with a simple class of planer ODEs which exhibit blow-up for some initial data. I will show how careful balancing of the dynamics near the unstable manifold with the noise will lead to stable longtime behavior. While system will exhibit intermittent behavior with a fat-tailed invariant distribution, it will converge exponentially fast to equilibrium. The proofs will turn on building a optimal Lyapunov function using associated Poisson equations.

If time permits, I will discuss some other examples of stabilization by noise including possibly Hamiltonian dynamics with a singular potential and the example of selection of long term statistics by the addition of noise. The last example is a toy version of the selection of an unique invariant measure in the inviscid limit of a stochastic PDE.

Date: Thursday, April 9, 2015
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  David Kinderlehrer