Small noise perturbations in dynamical systems: two applications in rare event simulation and pattern formation
Time and place
3 PM on Wednesday, February 25th, 2015; SH 377
Chia Lee (University of British Columbia)
Abstract
Random perturbations of dynamical systems have been a broad area of interest, fueled by its applicability in physics, computational chemistry and biology. In this talk, we discuss two active areas in the study of small noise perturbations. First of these is small noise diffusions in the context of large deviation theory and rare event simulation. The theory of large deviations, a la Wentzell-Freidlin theory, provides a rich theory of the exponential rates of small probabilities. We show how the theory can be exploited for the purpose of designing optimal importance sampling estimators for the efficient sampling and estimation of rare event probabilities, and in particular address the case of reflected diffusions, as arises in the context of queue buffer overflows in queuing networks. In the second topic, we will look at small noise perturbations in pattern forming dynamical systems. Originally derived to describe convective instability in the Rayleigh-Bernard model but now considered the prototypical model equation in pattern formation, the Swift-Hohenberg equation is known to develop slowly varying spatial patterns across a bifurcation. Further considering the interaction of delayed feedback control and small noise in the Swift-Hohenberg equation, we show how new oscillatory behavior are being excited by the delay and frequencies on multiple time scales sustained by the noise.
