Stochastic properties of solution for a chemostat model with a distributed delay and random disturbance  

作　　者：Xiaofeng Zhang Rong Yuan 

机构地区：[1]Laboratory of Mathematics and Complex Systems(Ministry of Education)School of Mathematical Sciences,Beijing Normal University Beijing 100875,People’s Republic of China

出　　处：《International Journal of Biomathematics》2020年第7期205-229,共25页生物数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.11771044 and 11871007).

摘　　要：In this paper,stochastic properties of solution for a chemostat model with a distributed delay and random disturbance are studied,and we use distribution delay to simulate the delay in nutrient conversion.By the linear chain technique,we transform the stochastic chemostat model with weak kernel into an equivalent degenerate system which contains three equations.First,we state that this model has a unique global positive solution for any initial value,which is helpful to explore its stochastic properties.Furthermore,we prove the stochastic ultimate boundness of the solution of system.Then sufficient conditions for solution of the system tending toward the boundary equilibrium point at exponential rate are established,which means the microorganism will be extinct.Moreover,we also obtain some sufficient conditions for ergodicity of solution of this system by constructing some suitable stochastic Lyapunov functions.Finally,we provide some numerical examples to illustrate theoretical results,and some conclusions and analysis are given.

关 键 词：Stochastic chemostat model distributed delay stochastic properties stochastically ultimate boundedness ERGODICITY 

分 类 号：O17[理学—数学]