Escape over a saddle by coloured noise: theory and numerics

Abstract

Stochastic dynamical systems allow modelling of transitions induced by disturbances, in particular from an attracting equilibrium and crossing the stable manifold of a saddle. In the small-noise limit, the probability of such transitions is governed by a large deviation principle. We illustrate a computational approach-the Method of Division-for approximating rare transition events, including their most likely paths, transition rates, and associated probabilities. To cater for realistic applications, we allow unbounded time, coloured and degenerate forcing. Its effectiveness is demonstrated on two examples: an inverted double-well potential and a simplified roll-heave ship capsize model.