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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

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Official URL: https://doi.org/10.1088/1742-5468/aa85cb

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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
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:
DateEvent
25 September 2017Published
7 August 2017Accepted
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
Funder: National Science Foundation (U.S.) (NSF)
Grant number: DMR-1420073, DMS-1522767

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