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

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, f...

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Bibliographic Details
Published in:Mathematical problems in engineering 2017-01, Vol.2017 (2017), p.1-11
Main Authors: Zhang, Jian, Zhang, Tongqian, Miao, Anqi
Format: Article
Language:English
Subjects:
Applied mathematics
Computer simulation
Cultivation
Economic models
Eigenvalues
Endangered & extinct species
Equilibrium
Extinction
Growth rate
Mathematical functions
Microorganisms
Noise
Noise intensity
Nutrients
Stability analysis
Stochastic models
Systems science
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Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2017/5217027