Stochastic models for chemically reacting systems using polynomial stochastic hybrid systems
Stochastic models for chemically reacting systems using polynomial stochastic hybrid systems
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DOI：
10.1002/rnc.1017
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发表时间：
2005-10-01
影响因子：
3.9
通讯作者：
Singh, A
中科院分区：
文献类型：
--
作者：
Hespanha, JP;Singh, A
本文提出了一个化学反应的随机模型，它把参与化学反应的各种物种的种群表示为一个多项随机混杂系统（pSHS）的连续状态。pSHS对应于具有多项式连续向量场、重置映射和过渡强度的随机混合系统。我们表明，pSHS，其连续状态的统计矩的动态，根据无穷维线性常微分方程（ODE），可以近似为任意精度的有限维非线性常微分方程。在此基础上，给出了建立这类近似的一个过程，并将此过程用于构造文献中出现的各种化学反应的近似随机模型。这些反应包括一个简单的双分子反应，其中一个可以解决的主方程;衰变二聚反应集，表现出两个不同的时间尺度;反应的化学速率方程有一个连续的平衡点;和Schogl反应。近似模型的准确性进行了研究，通过比较Monte Carlo模拟或主方程的解决方案，当可用的。版权所有（c）2005年约翰威利父子有限公司。
A stochastic model for chemical reactions is presented, which represents the population of various species involved in a chemical reaction as the continuous state of a polynonmial stochastic hybrid system (pSHS). pSHSs correspond to stochastic hybrid systems with polynomial continuous vector fields, reset maps, and transition intensities. We show that for pSHSs, the dynamics of the statistical moments of its continuous states, evolves according to infinite-dimensional linear ordinary differential equations (ODEs), which can be approximated by finite-dimensional nonlinear ODEs with arbitrary precision. Based on this result, a procedure to build this types of approximation is provided.This procedure is used to construct approximate stochastic models for a variety of chemical reactions that have appeared in literature. These reactions include a simple bimolecular reaction, for which one can solve the Master equation; a decaying-dimerizing reaction set which exhibits two distinct time scales; a reaction for which the chemical rate equations have a continuum of equilibrium points; and the bistable Schogl reaction. The accuracy of the approximate models is investigated by comparing with Monte Carlo simulations or the solution to the Master equation, when available. Copyright (c) 2005 John Wiley & Sons, Ltd.