具有多个参数扰动的随机恒化器模型的持久性与灭绝性
Exclusion and Persistence in Chemostat Model with Stochastic Perturbation on Multiple Parameters
考虑了一类营养基输入浓度和营养转化率同时受到白噪声干扰的随机恒化器模型. 首先应用随机微分方程的比较原理证明了模型正解的全局存在性和唯一性. 其次通过构造Lyapunov函数, 利用伊藤公式和随机微分方程的一些结论 研究了随机系统的持久性和灭绝性. 最后通过数值模拟验证了所得结果的正确性.
This paper deals with the problem of the single-species stochastic chemostat model. In this model, we assume that the nutrient input concentration and the nutrition conversion rate are influenced by white noises. The global existence and uniqueness of the positive solution of the system are proved by using stochastic comparison theorem. By constructing stochastic Lyapunov function, using It\^{o}'s formula and some theorems of stochastic differential equation, we show the persistence of the system and the extinction of the microorganism. Finally, numerical simulations are carried out to illustrate the theoretical results.
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