Journal
JOURNAL OF CHEMICAL PHYSICS
Volume 140, Issue 12, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.4867786
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Funding
- Engineering and Physical Sciences Research Council (EPSRC)
- Engineering and Physical Sciences Research Council [1086864] Funding Source: researchfish
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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. (C) 2014 AIP Publishing LLC.
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