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

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.

14 pages, 9 figures

References in corpus (3)

• Oscillatory Dynamics in Rock-Paper-Scissors Games with Mutations
• How limit cycles and quasi-cycles are related in systems with intrinsic noise
• Effects of intrinsic fluctuations in a prototypical chemical oscillator: metastability and switching

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