The Barrier Method: A Technique for Calculating Very Long Transition Times

TL;DR

The paper introduces the Barrier Method, a rapid numerical technique for accurately calculating very long transition times in low-dimensional dynamical systems, including non-equilibrium and epidemiological models.

Contribution

It presents a novel, efficient approach for computing rare-event transition times in systems lacking detailed balance, applicable to diverse scientific fields.

Findings

Successfully applied to a bistable non-equilibrium system.

Effective in a two-dimensional epidemiology model.

Achieves fast computation of very small transition rates.

Abstract

In many dynamical systems there is a large separation of time scales between typical events and "rare" events which can be the cases of interest. Rare-event rates are quite difficult to compute numerically, but they are of considerable practical importance in many fields: for example transition times in chemical physics and extinction times in epidemiology can be very long, but are quite important. We present a very fast numerical technique that can be used to find long transition times (very small rates) in low-dimensional systems, even if they lack detailed balance. We illustrate the method for a bistable non-equilibrium system introduced by Maier and Stein and a two-dimensional (in parameter space) epidemiology model.