Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (6): 1912-1924.

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Global Dynamics of a Stochastic Chemostat Model with General Response Function and Wall Growth

Liya Liu1(),Daqing Jiang1,2,*()   

  1. 1 School of Petroleum Engineering, Key Laboratory of Unconventional Oil & Gas Development, China University of Petroleum (East China), Ministry of Education, Shandong Qingdao 266580
    2 College of Science, China University of Petroleum, Shandong Qingdao 266580
  • Received:2020-08-20 Online:2021-12-26 Published:2021-12-02
  • Contact: Daqing Jiang;
  • Supported by:
    the NSFC(11871473);the Fundamental Research Funds for the Central Universities(15CX08011A)


This paper deals with problems of a stochastic chemostat model with general response function and wall growth. We show the conditions for the microorganism to be extinct. On the other hand, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the model which means the microorganism can become persistent. Finally, example and numerical simulations are introduced to illustrate the analytical results.

Key words: Chemostat, Wall growth, Extinction, Stationary distribution, General response functions

CLC Number: 

  • O211.63