Enhancing noise-induced switching times in systems with distributed delays

TL;DR

This paper develops a variational approach to calculate noise-induced switching times in systems with delay-distributed kernels, revealing how distribution width influences switching durations, with analytical results validated by simulations.

Contribution

It introduces a general variational formulation for switching rates in systems with delay-distributed kernels, providing explicit analytical results for small delays and demonstrating the impact of distribution width.

Findings

Increasing distribution width prolongs switching times.

Analytical results match numerical simulations.

Two-peak distributions have a greater effect on switching times.

Abstract

The paper addresses the problem of calculating the noise-induced switching rates in systems with delay-distributed kernels and Gaussian noise. A general variational formulation for the switching rate is derived for any distribution kernel, and the obtained equations of motion and boundary conditions represent the most probable, or optimal, path, which maximizes the probability of escape. Explicit analytical results for the switching rates for small mean time delays are obtained for the uniform and bi-modal (or two-peak) distributions. They suggest that increasing the width of the distribution leads to an increase in the switching times even for longer values of mean time delays for both examples of the distribution kernel, and the increase is higher in the case of the two-peak distribution. Analytical predictions are compared to the direct numerical simulations, and show excellent agreement between theory and numerical experiment.