Quasipotentials for coupled escape problems and the gate-height bifurcation

Peter Ashwin, Jennifer Creaser, and Krasimira Tsaneva-Atanasova
Phys. Rev. E 107, 014213 – Published 23 January 2023
PDFHTMLExport Citation

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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
3 More
  • Received 27 September 2022
  • Accepted 21 December 2022

DOI:https://doi.org/10.1103/PhysRevE.107.014213

©2023 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear Dynamics

Authors & Affiliations

Peter Ashwin and Jennifer Creaser

  • Department of Mathematics and Statistics, University of Exeter, Exeter EX4 4QF, United Kingdom

Krasimira Tsaneva-Atanasova

  • Department of Mathematics and Statistics, and EPSRC Hub for Quantitative Modelling in Healthcare, University of Exeter, Exeter EX4 4QJ, United Kingdom and Institute for Advanced Study, Technical University of Munich, Lichtenbergstrasse 2 a, D-85748 Garching, Germany

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 107, Iss. 1 — January 2023

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×