Noise-Induced Stabilization of Perturbed Hamiltonian Systems

Noise-induced stabilization is the phenomenon in which the addition of randomness to an unstable system of ordinary differential equations results in a stable system of stochastic differential equations. With stability defined as global stochastic boundedness, Hamiltonian systems can never be stabilized by the addition of noise that is constant in space. In this article, we investigate how to deterministically perturb a class of unstable Hamiltonian systems in such a way that the qualitative behavior is preserved, but that enables the systems to exhibit noise-induced stabilization