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The Stochastic Periodic Behavior of a Chemostat Model with Periodic Nutrient Input

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Abstract

In this paper, we study the stochastic periodic behavior of a chemostat model with periodic nutrient input. We first prove the existence of global unique positive solution with any initial value for stochastic non-autonomous periodic chemostat system. After that, the sufficient conditions are established for the existence of nontrivial positive \(T-\)periodic solution. Moreover, we also analyze the conditions for extinction exponentially of microorganism, and we find that there exists a unique boundary periodic solution for stochastic chemostat model, which is globally attractive. At the same time, in the end of this paper, we also give some numerical simulations to illustrate our main conclusions.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 12171039) and the Fundamental Research Funds for the Central Universities (No. 2021NTST03).

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Authors and Affiliations

  1. Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China

    Xiaofeng Zhang & Rong Yuan

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  1. Xiaofeng Zhang
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  2. Rong Yuan
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Correspondence to Xiaofeng Zhang.

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Communicated by See Keong Lee.

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Zhang, X., Yuan, R. The Stochastic Periodic Behavior of a Chemostat Model with Periodic Nutrient Input. Bull. Malays. Math. Sci. Soc. 46, 165 (2023). https://doi.org/10.1007/s40840-023-01557-4

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