3:00 p.m., Monday (Feb. 4)
Math Annex 1100
University of Minnesota
Stochastic dynamics in models sensitive to noise
Many systems which are sensitive to noise exhibit
dynamical features from both the underlying
deterministic behavior and the stochastic elements.
Then the stochastic effects are obscured in this mix
of dynamics. Several different methods have recently
been applied to separate the "deterministic" and "stochastic"
dynamics. These approaches lead to simplified approximate
models which can be analyzed or simulated efficiently,
providing useful measures of the noise sensitivity.
The methods combine projection methods and the identification
of important scaling relationships to exploit features common
to these systems, such as the presence of multiple time scales,
limited regions of strong noise-sensitivity, and resonances.
These approaches are valuable for studying a variety of problems,
including stochastic delay-differential equations, noisy bursters,
and meta-stable interfaces. The approach will be outlined in one
or two of these applications, and the generalization to other areas
will be discussed. The results have interesting connections to
classical probabilistic methods, dynamical systems analysis,
and singular perturbation theory.