Long-Time Behavior and Density Function of a Stochastic Chemostat Model with Degenerate Diffusion  

作　　者：GAO Miaomiao JIANG Daqing WEN Xiangdan 

机构地区：[1]College of Science,China University of Petroleum(East China),Qingdao 266580,China [2]Key Laboratory of Unconventional Oil and Gas Development,China University of Petroleum(East China),Ministry of Education,Qingdao 266580,China [3]Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group,Department of Mathematics,King Abdulaziz University,Jeddah 21589,Saudi Arabia [4]Department of Mathematics,Yanbian University,Yanji 133002,China

出　　处：《Journal of Systems Science & Complexity》2022年第3期931-952,共22页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant No.11871473;the Natural Science Foundation of Shandong Province under Grant No.ZR2019MA010;the Science and Technology Research Project of Jilin Provincial Department of Education of China under Grant No.JJKH20180462KJ。

摘　　要：This paper considers a stochastic chemostat model with degenerate diffusion.Firstly,the Markov semigroup theory is used to establish sufficient criteria for the existence of a unique stable stationary distribution.The authors show that the densities of the distributions of the solutions can converge in L^(1)to an invariant density.Then,conditions are obtained to guarantee the washout of the microorganism.Furthermore,through solving the corresponding Fokker-Planck equation,the authors give the exact expression of density function around the positive equilibrium of deterministic system.Finally,numerical simulations are performed to illustrate the theoretical results.

关 键 词：Density function diffusion process Markov semigroups stochastic chemostat model WASHOUT 

分 类 号：O211.6[理学—概率论与数理统计]