具有单调功能反应函数的随机恒化器模型的动力学行为

Dynamics of a Stochastic Chemostat Model with a Monotone Response Function

考虑到环境噪声对微生物连续培养的影响,研究了一类流出率受环境噪声扰动的具有单调功能反应函数的恒化器模型.利用随机微分方程比较定理得到了全局正解的存在唯一性定理;通过构造Lyapunov函数,证明了绝灭平衡点是随机全局渐近稳定的;证明了当噪声强度较小时,系统的解将围绕相应确定性模型的正平衡点振荡;当噪声强度较大时,噪声会引起微生物的整体溢出.所得模型及结论将现有结果推广至单调功能反应函数情形.

We construct a stochastic chemostat model with a monotone response function,where the dilution rate is influenced by white noises. The global existence and unique of the positive solution are obtained. Using Lyapunov function,we show that the washout equilibrium is stochastically stable. Then we show that the solution of the stochasticmodel spirals around the corresponding positive equilibrium of the deterministic model when the noise intensity is less than some values. When the noise is large enough,the microorganism will be washed out in the chemostat. The models and results are extended to the cases with monotone response function.