Numerical methods for identifying hyperbolic periodic orbits and characterizing rare events in nongradient systems
摘要：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.
20170801陶默雷Numerical methods for identifying hyperbolic periodic orbits and characterizing rare events in nongradient systems