2013/12/31 by Tobias Brett, Tobias Galla
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Approximations of π #Brusselator #Formalism (music) #Gaussian #Gene Regulatory Network Analysis #Langevin dynamics #Langevin equation #Nonlinear Dynamics and Pattern Formation #Stochastic differential equation #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1063/1.4867786
published as J. Chem. Phys. 140, 124112 (2014) · 14 pages, 9 figures
arxiv created 2014/03/25 · openalex publication_date 2014/03/28 · arxiv updated 2014/06/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.