一类具有单调功能反应函数的随机恒化器模型的渐近行为分析

Asymptotic Behavior of A Stochastic Chemostat Model With A Monotone Response Functions

考虑到环境噪声对系统的整体影响,建立一类具有单调功能反应函数的随机恒化器模型。利用It公式验证随机模型正解的全局存在唯一性;通过构造Lyapunov函数,证明当噪声强度较小时,系统的解将围绕相应确定性模型的平衡点振荡;最后,根据Hasminskii定理证明系统平稳分布的存在性。所得模型及结论将现有结果推广至一般情形。

We construct a stochastic Chemostat model with a monotone response functions,where stochastic perturbations are a white noise type which are directly proportional to the density of microorganism and substrate. By using the It8 formula,we obtain the global existence and unique of the positive solution. Then we show that the solution of the stochastic model spirals around the corresponding equilibrium of the deterministic model when the noise intensity is less than some values. Finally,we prove that there exists a stationary distribution by use of the Hasminskii theorem. Our models and results are extended to the general case.