Vol. 14, No. 2, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Volume 15, Issue 2
Volume 15, Issue 1
Volume 14, Issue 2
Volume 14, Issue 1
Volume 13, Issue 2
Volume 13, Issue 1
Volume 12, Issue 1
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 1
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 1
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 1
Volume 3, Issue 1
Volume 2, Issue 1
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
Author Index
To Appear
Other MSP Journals
Computing the quasipotential for highly dissipative and chaotic SDEs an application to stochastic Lorenz'63

Maria Cameron and Shuo Yang

Vol. 14 (2019), No. 2, 207–246

The study of noise-driven transitions occurring rarely on the time scale of systems modeled by SDEs is of crucial importance for understanding such phenomena as genetic switches in living organisms and magnetization switches of the Earth. For a gradient SDE, the predictions for transition times and paths between its metastable states are done using the potential function. For a nongradient SDE, one needs to decompose its forcing into a gradient of the so-called quasipotential and a rotational component, which cannot be done analytically in general.

We propose a methodology for computing the quasipotential for highly dissipative and chaotic systems built on the example of Lorenz’63 with an added stochastic term. It is based on the ordered line integral method, a Dijkstra-like quasipotential solver, and combines 3D computations in whole regions, a dimensional reduction technique, and 2D computations on radial meshes on manifolds or their unions. Our collection of source codes is available on M. Cameron’s web page and on GitHub.

quasipotential, ordered line integral method, Lorenz'63, maximum likelihood transition path
Mathematical Subject Classification 2010
Primary: 65N99, 65P99, 58J65
Received: 22 November 2018
Revised: 15 June 2019
Accepted: 16 July 2019
Published: 4 October 2019
Maria Cameron
Department of Mathematics
University of Maryland, College Park
College Park, MD
United States
Shuo Yang
Department of Mathematics
University of Maryland, College Park
College Park, MD
United States