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

Tobias Brett, Tobias Galla

    Research output: Contribution to journalArticlepeer-review

    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. (C) 2014 AIP Publishing LLC.
    Original languageEnglish
    Article number12412
    Number of pages12
    JournalThe Journal of chemical physics
    Volume140
    Issue number12
    DOIs
    Publication statusPublished - 2014

    Fingerprint

    Dive into the research topics of 'Gaussian approximations for stochastic systems with delay: Chemical Langevin equation and application to a Brusselator system'. Together they form a unique fingerprint.

    Cite this