Quasipotentials for coupled escape problems and the gate-height bifurcation

Abstract

The escape statistics of a gradient dynamical system perturbed by noise can be estimated using properties of the associated potential landscape. More generally, the Freidlin and Wentzell quasipotential (QP) can be used for similar purposes, but computing this is nontrivial and it is only defined relative to some starting point. In this paper we focus on computing quasipotentials for coupled bistable units, numerically solving a Hamilton- Jacobi-Bellman type problem. We analyze noise induced transitions using the QP in cases where there is no potential for the coupled system. Gates (points on the boundary of basin of attraction that have minimal QP relative to that attractor) are used to understand the escape rates from the basin, but these gates can undergo a global change as coupling strength is changed. Such a global gate-height bifurcation is a generic qualitative transition in the escape properties of parametrized nongradient dynamical systems for small noise.