Activated escape of periodically modulated systems

TL;DR

This paper investigates how noise-induced escape rates in periodically modulated overdamped systems vary with modulation amplitude, revealing complex behaviors including nonmonotonic prefactors and distinct scaling regimes near bifurcation points.

Contribution

It provides a comprehensive analysis of escape rates for arbitrary modulation amplitudes, identifying three distinct scaling regimes and detailed behavior of the prefactor.

Findings

Escape rate peaks vary from Gaussian to asymmetric with modulation.

Prefactor depends nonmonotonically on amplitude A.

Scaling of the prefactor near bifurcation amplitude A_c follows three regimes with exponents 1/4, -1, and 1/2.

Abstract

The rate of noise-induced escape from a metastable state of a periodically modulated overdamped system is found for an arbitrary modulation amplitude $A$. The instantaneous escape rate displays peaks that vary with the modulation from Gaussian to strongly asymmetric. The prefactor $\nu$ in the period-averaged escape rate depends on $A$ nonmonotonically. Near the bifurcation amplitude $A_c$ it scales as $\nu\propto (A_c-A)^{\zeta}$. We identify three scaling regimes, with $\zeta = 1/4, -1$, and 1/2.