Small-Noise-Induced Metastable Transition of Periodically Perturbed Systems

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 961-981, March 2024.
Abstract. This work is devoted to investigating the noise-induced rare transition of periodically driven systems. The maximum likelihood paths (MLPs) are often sought, in order to reveal the transition mechanism. We show that MLPs between metastable periodic states could persist to a small nonautonomous forcing under appropriate conditions. Furthermore, we obtain a closed-form explicit expression for approximating the transition rate change. They are obtained based on standard perturbation techniques for the Euler–Lagrange equation, the Melnikov theory, as well as a linear-theory calculation. Our methods indicate a route for a detailed understanding for the interaction between periodic forcing and noise in rather general systems.