event
Tuesday 18 Apr 2023: Uncertainty Quantification near Stochastically Perturbed Limit Cycles and Tori Using COCO-Compatible Boundary-Value Problems
Harry Dankowicz - University of Illinois, Urbana-Champaign
Laver LT6 14:30-15:30
In this talk, I discuss long-term noise-induced dynamics near transversally stable periodic orbits (limit cycles) and quasiperiodic invariant tori of arbitrary dimension in the small noise limit of the corresponding stochastic differential equations. I demonstrate how the dynamics may be quantified in terms of a novel covariance boundary-value problem that characterizes the Gaussian restrictions of a stationary distribution to transversal hyperplanes that are invariant under the linearized flow near the limit cycle or torus. In addition to closed-form solutions, I discuss numerical implementations in the software package COCO for performing parameter continuation along families of limit cycles or tori and simultaneously quantifying the stochastic dynamics. Several model examples concerned with the analysis of limit cycles and two-dimensional invariant tori are used to illustrate the predictive power of the methodology and the ease with which the technique may be reduced to code using COCO.
