Quasipotentials for coupled escape problems and the gate-height bifurcation

TL;DR

This paper develops numerical methods to compute quasipotentials for coupled bistable systems, revealing how escape dynamics and gate structures change with coupling strength, especially through a global gate-height bifurcation.

Contribution

It introduces a numerical approach for quasipotential computation in coupled systems and analyzes the gate-height bifurcation affecting escape properties.

Findings

Numerical methods for quasipotential computation in coupled systems.

Identification of a global gate-height bifurcation.

Escape properties are qualitatively altered by the 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 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.