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Abstract
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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.
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Keywords
quasipotential, ordered line integral method, Lorenz'63,
maximum likelihood transition path
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Mathematical Subject Classification 2010
Primary: 65N99, 65P99, 58J65
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Milestones
Received: 22 November 2018
Revised: 15 June 2019
Accepted: 16 July 2019
Published: 4 October 2019
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