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Title: Gaussian approximations for stochastic systems with delay: Chemical Langevin equation and application to a Brusselator system

We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.
Authors:
;  [1]
  1. Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL (United Kingdom)
Publication Date:
OSTI Identifier:
22253356
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 140; Journal Issue: 12; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; GAUSS FUNCTION; INTEGRO-DIFFERENTIAL EQUATIONS; LANGEVIN EQUATION; MARKOV PROCESS