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Non-equilibrium transitions between metastable fixed-points in slow-fast systems with a bifurcating slow manifold
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Grafke, Tobias and Vanden-Eijnden, Eric (2017) Non-equilibrium transitions between metastable fixed-points in slow-fast systems with a bifurcating slow manifold. Journal of Statistical Mechanics : Theory and Experiment, 2017 . 093208. doi:10.1088/1742-5468/aa85cb ISSN 1742-5468.
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Official URL: https://doi.org/10.1088/1742-5468/aa85cb
Abstract
Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed within the realm of large deviation theory. It is shown that these non-equilibrium transitions make use of a reaction channel created by the bifurcation structure of the slow manifold, leading to vastly increased transition rates. Several examples are used to illustrate these findings, including an insect outbreak model, a system modeling phase separation in the presence of evaporation, and a system modeling transitions in active matter self-assembly. The last example involves a spatially extended system modeled by a stochastic partial differential equation.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Manifolds (Mathematics), Bifurcation theory | ||||||
Journal or Publication Title: | Journal of Statistical Mechanics : Theory and Experiment | ||||||
Publisher: | Institute of Physics Publishing Ltd. | ||||||
ISSN: | 1742-5468 | ||||||
Official Date: | 25 September 2017 | ||||||
Dates: |
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Volume: | 2017 | ||||||
Article Number: | 093208 | ||||||
DOI: | 10.1088/1742-5468/aa85cb | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 4 October 2017 | ||||||
Date of first compliant Open Access: | 5 October 2017 | ||||||
Funder: | National Science Foundation (U.S.) (NSF) | ||||||
Grant number: | DMR-1420073, DMS-1522767 |
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