We analyze the fluctuationdriven escape of particles from a metastable state under the influence of a weak periodic force. We develop an asymptotic method to solve the appropriate Fokker–Planck equation with mixed natural and absorbing boundary conditions. The approach uses two boundary layers flanking an interior region; most of the probability is concentrated within the boundary layer near the metastable point of the potential and particles transit the interior region before exiting the domain through the other boundary layer, which is near the unstable maximal point of the potential. The dominant processes in each region are given by approximate timedependent solutions matched to construct the approximate composite solution, which gives the rate of escape with weak periodic forcing. Using reflection we extend the method to a double well potential influenced by white noise and weak periodic forcing, and thereby derive a twostate stochastic model—the simplest treatment of stochastic resonance theory—in the nonadiabatic limit.
This content will become publicly available on February 1, 2025
 NSFPAR ID:
 10500535
 Publisher / Repository:
 Springer Link
 Date Published:
 Journal Name:
 Journal of Mathematical Fluid Mechanics
 Volume:
 26
 Issue:
 1
 ISSN:
 14226928
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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