木糖醇发酵的随机延迟微分方程模型分析

Model Analysis of Stochastic Delay Differential Equations for Xylitol Fermentation

在经典木糖醇发酵模型的基础上,引入布朗运动模拟发酵过程中客观存在的随机干扰因素,且考虑到发酵过程的迟滞性,从而构造了木糖醇发酵的随机延迟微分方程模型并证明了该模型全局正解的存在性、随机最终有界性和渐近性质。应用数值实验验证了模型的实际可行性。

On the basis of the classical xylitol fermentation models,the xylitol fermentation model of stochastic delay differential equations is constructed in the presence of Brown motion to simulate the objective stochastic factors and considerate the fermentation delay. The existence of the global positive solutions, stochastic uhimate boundedness and asymptotic property were given for such model. The feasibility of the model was verified through the numerical experiments.