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Mathematical Problems in Engineering
Volume 2017, Article ID 5217027, 11 pages
https://doi.org/10.1155/2017/5217027
Research Article

Threshold Dynamics of a Stochastic Chemostat Model with Two Nutrients and One Microorganism

1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
2State Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China

Correspondence should be addressed to Tongqian Zhang; nc.ude.tsuds@naiqgnotgnahz

Received 30 March 2017; Revised 15 July 2017; Accepted 20 August 2017; Published 25 September 2017

Academic Editor: Zhongwei Lin

Copyright © 2017 Jian Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new stochastic chemostat model with two substitutable nutrients and one microorganism is proposed and investigated. Firstly, for the corresponding deterministic model, the threshold for extinction and permanence of the microorganism is obtained by analyzing the stability of the equilibria. Then, for the stochastic model, the threshold of the stochastic chemostat for extinction and permanence of the microorganism is explored. Difference of the threshold of the deterministic model and the stochastic model shows that a large stochastic disturbance can affect the persistence of the microorganism and is harmful to the cultivation of the microorganism. To illustrate this phenomenon, we give some computer simulations with different intensity of stochastic noise disturbance.