Title
Noise-Induced Stabilization of Hamiltonian Systems
Faculty Sponsor
Dr. Tiffany Kolba
College
Arts and Sciences
Department/Program
Mathematics and Statistics
ORCID Identifier(s)
0000-0002-0834-1876 0000-0003-3662-4846 0000-0003-1216-3424
Presentation Type
Poster Presentation
Symposium Date
Summer 7-29-2019
Abstract
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.
Recommended Citation
Meskill, Daniel; Garner, Julia; and Hughes, Victor G., "Noise-Induced Stabilization of Hamiltonian Systems" (2019). Summer Interdisciplinary Research Symposium. 53.
https://scholar.valpo.edu/sires/53
Biographical Information about Author(s)
Daniel Meskill is a rising junior majoring in mathematics and statistics at the University of Connecticut. He is interested in probability theory and statistical applications. After completing his bachelor's degree, he plans to attend graduate school in pursuit of a PhD in statistics.
Julia Garner is a senior majoring in mathematics at College of Coastal Georgia. Some of her mathematical interests include differential equations and stochastic processes. She plans to pursue her PhD in mathematics after obtaining her bachelor's degree.
Victor Hughes is a rising senior majoring in Applied Mathematics at Purdue University. His mathematical interests are differential equations, stochastic processes, and dynamical systems. After acquiring his bachelor's degree, he plans on pursuing a PhD in Applied Mathematics.