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Title: Model reduction for slow–fast stochastic systems with metastable behaviour

Abstract

The quasi-steady-state approximation (or stochastic averaging principle) is a useful tool in the study of multiscale stochastic systems, giving a practical method by which to reduce the number of degrees of freedom in a model. The method is extended here to slow–fast systems in which the fast variables exhibit metastable behaviour. The key parameter that determines the form of the reduced model is the ratio of the timescale for the switching of the fast variables between metastable states to the timescale for the evolution of the slow variables. The method is illustrated with two examples: one from biochemistry (a fast-species-mediated chemical switch coupled to a slower varying species), and one from ecology (a predator–prey system). Numerical simulations of each model reduction are compared with those of the full system.

Authors:
 [1];  [1];  [2]
  1. Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom)
  2. Computational Science Laboratory, Microsoft Research, Cambridge CB1 2FB (United Kingdom)
Publication Date:
OSTI Identifier:
22252924
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 140; Journal Issue: 17; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; COMPUTERIZED SIMULATION; DEGREES OF FREEDOM; METASTABLE STATES; STOCHASTIC PROCESSES

Citation Formats

Bruna, Maria, Computational Science Laboratory, Microsoft Research, Cambridge CB1 2FB, Chapman, S. Jonathan, and Smith, Matthew J. Model reduction for slow–fast stochastic systems with metastable behaviour. United States: N. p., 2014. Web. doi:10.1063/1.4871694.
Bruna, Maria, Computational Science Laboratory, Microsoft Research, Cambridge CB1 2FB, Chapman, S. Jonathan, & Smith, Matthew J. Model reduction for slow–fast stochastic systems with metastable behaviour. United States. https://doi.org/10.1063/1.4871694
Bruna, Maria, Computational Science Laboratory, Microsoft Research, Cambridge CB1 2FB, Chapman, S. Jonathan, and Smith, Matthew J. 2014. "Model reduction for slow–fast stochastic systems with metastable behaviour". United States. https://doi.org/10.1063/1.4871694.
@article{osti_22252924,
title = {Model reduction for slow–fast stochastic systems with metastable behaviour},
author = {Bruna, Maria and Computational Science Laboratory, Microsoft Research, Cambridge CB1 2FB and Chapman, S. Jonathan and Smith, Matthew J.},
abstractNote = {The quasi-steady-state approximation (or stochastic averaging principle) is a useful tool in the study of multiscale stochastic systems, giving a practical method by which to reduce the number of degrees of freedom in a model. The method is extended here to slow–fast systems in which the fast variables exhibit metastable behaviour. The key parameter that determines the form of the reduced model is the ratio of the timescale for the switching of the fast variables between metastable states to the timescale for the evolution of the slow variables. The method is illustrated with two examples: one from biochemistry (a fast-species-mediated chemical switch coupled to a slower varying species), and one from ecology (a predator–prey system). Numerical simulations of each model reduction are compared with those of the full system.},
doi = {10.1063/1.4871694},
url = {https://www.osti.gov/biblio/22252924}, journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 17,
volume = 140,
place = {United States},
year = {Wed May 07 00:00:00 EDT 2014},
month = {Wed May 07 00:00:00 EDT 2014}
}