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

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  • Jian Zhang
  • Anqi Miao
  • Tongqian Zhang

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.

Suggested Citation

  • Jian Zhang & Anqi Miao & Tongqian Zhang, 2017. "Threshold Dynamics of a Stochastic Chemostat Model with Two Nutrients and One Microorganism," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-11, September.
    • Handle: RePEc:hin:jnlmpe:5217027
    DOI: 10.1155/2017/5217027
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