  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 non-trivial 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 analyse 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 transitions in the
escape properties of parametrised non-gradient dynamical systems for small
noise.
