Noise-Induced Stabilization of Hamiltonian Systems
Dr. Tiffany Kolba
Arts and Sciences
Mathematics and Statistics
0000-0002-0457-5077 0000-0001-6604-2367 0000-0003-1986-7336
Noise-induced stabilization is the phenomenon in which the addition of randomness to an unstable deterministic system of ordinary differential equations (ODEs) results in a stable system of stochastic differential equations (SDEs). A Hamiltonian system is a two-dimensional system of ODEs defined by a Hamiltonian function, which is constant along each solution curve. With stability defined as global stochastic boundedness, Hamiltonian systems cannot be stabilized by the addition of noise that is constant in space. Therefore we seek to deterministically perturb the Hamiltonian systems in such a way that the qualitative behavior of solutions is preserved, but noise-induced stabilization becomes possible. Our goal is to provide a systematic framework for methods of perturbing the systems and proving noise-induced stabilization.
Coniglio, Anthony; Sparks, Sarah; and Weithers, Daniel, "Noise-Induced Stabilization of Hamiltonian Systems" (2017). Summer Interdisciplinary Research Symposium. 18.