Noise-Induced Stabilization of Hamiltonian Systems
Dr. Tiffany Kolba
Arts and Sciences
Mathematics and Statistics
0000-0002-0834-1876 0000-0003-3662-4846 0000-0003-1216-3424
Noise-induced stabilization is the phenomenon where a system of ordinary differential equations is unstable, but by adding randomness, its corresponding system of stochastic differential equations is stable. It has been proven that unstable Hamiltonian systems cannot be stabilized by adding constant noise, where global stochastic boundedness is our notion of stability. In this study, we investigate adding nonconstant noise to two classes of Hamiltonian systems to achieve noise-induced stabilization. Our method for proving noise-induced stabilization consists of constructing local Lyapunov functions on various subsets of the plane, and then smoothing them together to form a global Lyapunov function defined on the entire plane. We also pursue the minimum noise necessary for stabilization of these systems.
Meskill, Daniel; Garner, Julia; and Hughes, Victor G., "Noise-Induced Stabilization of Hamiltonian Systems" (2019). Summer Interdisciplinary Research Symposium. 53.