Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems
Name
PhysRevE.94.032212.pdf
Size
5.63 MB
Format
Adobe PDF
Checksum (MD5)
dc9032864b6709ff6cb6c969a00c70c1
Author(s)
Farazmand, Mohammad M
Sapsis, Themistoklis P.
Date Issued
September 2016
Journal
Physical Review E
Publisher
American Physical Society
Citation
Farazmand, Mohammad, and Themistoklis P. Sapsis. “Dynamical Indicators for the Prediction of Bursting Phenomena in High-Dimensional Systems.” Physical Review E 94.3 (2016): n. pag. © 2016 American Physical Society
Version
Final published version
Abstract
Drawing upon the bursting mechanism in slow-fast systems, we propose indicators for the prediction of such rare extreme events which do not require a priori known slow and fast coordinates. The indicators are associated with functionals defined in terms of optimally time-dependent (OTD) modes. One such functional has the form of the largest eigenvalue of the symmetric part of the linearized dynamics reduced to these modes. In contrast to other choices of subspaces, the proposed modes are flow invariant and therefore a projection onto them is dynamically meaningful. We illustrate the application of these indicators on three examples: a prototype low-dimensional model, a body-forced turbulent fluid flow, and a unidirectional model of nonlinear water waves. We use Bayesian statistics to quantify the predictive power of the proposed indicators.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.94.032212
