Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom.
J Chem Phys. 2014 Mar 28;140(12):124112. doi: 10.1063/1.4867786.
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.
我们提出了一种启发式推导，用于对具有分布延迟的随机化学反应系统进行高斯近似。特别是，我们推导出了相应的化学朗之万方程。由于基础动力学的非马尔可夫特征，这些方程是积分微分方程，并且高斯近似中的噪声是有色的。在化学朗之万方程的基础上，进一步的简化导致了线性噪声近似。我们将该形式应用于著名的布鲁塞尔振子模型的延迟变体，并展示了如何使用它来描述噪声驱动的准循环以及噪声触发的尖峰。我们发现准循环的典型频率对延迟周期的依赖性非常复杂。
