Analytical solution of stochastic resonance in the nonadiabatic regime

TL;DR

This paper extends the understanding of stochastic resonance beyond the adiabatic limit by deriving an analytical solution for the probability density function in the nonadiabatic regime, validated numerically, and enabling prediction of escape rates under complex forcing.

Contribution

It introduces a novel analytical approach to stochastic resonance in the nonadiabatic regime using a singular perturbation method, overcoming previous adiabatic limitations.

Findings

Analytical solution matches numerical simulations.

Predicts escape rates under complex periodic forcing.

Generalizes stochastic resonance beyond adiabatic conditions.

Abstract

We generalize stochastic resonance to the nonadiabatic limit by treating the double-well potential using two quadratic potentials. We use a singular perturbation method to determine an approximate analytical solution for the probability density function that asymptotically connects local solutions in boundary layers near the two minima with those in the region of the maximum that separates them. The validity of the analytical solution is confirmed numerically. Free from the constraints of the adiabatic limit, the approach allows us to predict the escape rate from one stable basin to another for systems experiencing a more complex periodic forcing.