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

Tobias Brett; Tobias Galla

doi:10.1063/1.4867786

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arXiv · 1312.2764

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

Tobias Brett·Tobias Galla

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Abstract

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.

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Tobias Brett, Tobias Galla. 2014-03-25. Gaussian approximations for stochastic systems with delay: chemical Langevin equation and application to a Brusselator system. https://doi.org/10.1063/1.4867786

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