基于平稳分布的随机恒化器动力学分析

Dynamic analysis of stochastic chemostat model based on stationary distribution

基于平稳分布,研究了一类带有参数扰动的随机恒化器模型的空间动力学行为。首先,利用微分方程的基本理论,求出微生物种群平稳分布概率密度函数的完全表达式;然后,对于所得的平稳分布密度函数的形态进行分析,发现噪声在很大程度上将改变原有确定性恒化器模型的动力学行为,而且最大概率平衡点会随噪声强度的改变而改变,呈现出较为复杂的动力学行为;最后,通过一组文献中的实验数值进行模拟分析,所得结论与理论结果一致。研究恒化器模型的主要目的是研究其中微生物的生存分布,对这一问题进行深入的研究,可为相关从业工作者提供较为完善的理论依据。

Based on the stationary distribution,the spatial dynamic behavior of a class of stochastic chemostat models with parameter perturbations is studied.Firstly,the complete expression of the probability density function of the stationary distribution of microbial population is obtained by using the basic theory of differential equation.Then,by analyzing the shape of the obtained stationary distribution density function,it is found that the noise changes the dynamic behavior of the original deterministic chemostat model to a large extent.In addition,the maximum probability equilibrium point will change with the change of noise intensity,presenting a relatively complex dynamic behavior.Finally,a group of experimental data in the literature are used to simulate and analyze the results,which are consistent with the theoretical results.The main purpose of studying the chemostat model is to study the survival and distribution of microorganisms in it.In-depth study on this problem can provide relatively complete theoretical basis for relevant practitioners.