Duncan Andrew, Liao Shuohao, Vejchodský Tomáš, Erban Radek, Grima Ramon
Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom.
Institute of Mathematics, Czech Academy of Sciences, Žitná 25, CZ-115 67, Czech Republic.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):042111. doi: 10.1103/PhysRevE.91.042111. Epub 2015 Apr 10.
The noisy dynamics of chemical systems is commonly studied using either the chemical master equation (CME) or the chemical Fokker-Planck equation (CFPE). The latter is a continuum approximation of the discrete CME approach. It has recently been shown that for a particular system, the CFPE captures noise-induced multistability predicted by the CME. This phenomenon involves the CME's marginal probability distribution changing from unimodal to multimodal as the system size decreases below a critical value. We here show that the CFPE does not always capture noise-induced multistability. In particular we find simple chemical systems for which the CME predicts noise-induced multistability, whereas the CFPE predicts monostability for all system sizes.
化学系统的噪声动力学通常使用化学主方程（CME）或化学福克 - 普朗克方程（CFPE）进行研究。后者是离散CME方法的连续近似。最近已经表明，对于特定系统，CFPE捕捉到了CME预测的噪声诱导的多稳态性。这种现象涉及随着系统规模减小到临界值以下，CME的边际概率分布从单峰变为多峰。我们在此表明，CFPE并不总是能捕捉到噪声诱导的多稳态性。特别是，我们发现了一些简单的化学系统，对于这些系统，CME预测了噪声诱导的多稳态性，而CFPE预测在所有系统规模下都是单稳态。
