Colloquium: Numerical identification of hyperbolic periodic orbits and characterization of rare events in nongradient systems
Numerical identification of hyperbolic periodic orbits and characterization of rare events in nongradient systems
Dr. Molei Tao, Assistant Professor, School of Mathematics, Georgia Institute of Technology
We consider stochastic dynamical systems modeled by differential equations perturbed by small noises. The goal is to quantify how noises can change the dynamics and possibly also utilize those effects.
More specifically, noise-induced dynamics are understood by maximizing transition probability characterized by Freidlin-Wentzell large deviation theory. In gradient systems (i.e., non-equilibrium
statistical mechanics modeled by reversible diffusion processes), metastable transitions were well understood and known to cross separatrices at saddle points. We investigate nongradient systems (which
may no longer be reversible; examples include stochastic mechanical systems and turbulent fluids), and show a very different type of transitions that cross hyperbolic periodic orbits.
Numerical tools for both identifying such periodic orbits and computing transition paths are described. If time permits, I will also discuss how these results may help design control strategies.