基于Markov链的重组细胞恒化培养的随机建模分析

Stochastic Modelling and Analysis of Recombinant Cell Chemostat Based on Markov Chains

本文研究了一类重组细胞恒化培养的连续时间Markov链模型.首先利用累积母函数表示出数字特征所满足的矩方程,然后通过对数正态分布近似的矩封闭技术得到了封闭后的矩方程,最后运用Euler-Maruyama方法构建了时间和状态都是连续的It随机微分方程.为了验证矩封闭的合理性,利用数值模拟给出了确定模型、随机模型和矩封闭后的方程的比较,并分析了重组细胞的变化趋势,结果表明其随机游走趋势与相应确定性模型是一致的.

In this paper, a class of continuous time Markov chain model for recombinant cell chemostat culture is investigated. Firstly, applying the cumulant generating function, the moment equations which the digital features satisfy are obtained. Then the moment closure equations are derived by the moment closure techniques based on the lognormal approxima- tion, and the corresponding Ito stochastic differential equations are given according to the Euler-Maruyama method. To illustrate the rationality of the moment closure, the numerical simulation is given to compare the deterministic model with the stochastic model and moment closure equations, and to analyze trends of the recombinant cell. The result shows that the behaviour of random work is consistent with the corresponding deterministic model.