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A Note on the Stationary Probability Density Function and Covariance Matrix of a Stochastic Chemostat Model with Distributed Delay

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Abstract

In this paper, we will focus on the stochastic chemostat model with distributed delay and Monod-type nutrient absorption function in Stratonovich form. We study some probabilistic properties of this stochastic chemostat model. By solving the corresponding Fokker-Planck equation of this model, we obtain the expression of joint density function near the positive equilibrium point of the deterministic chemostat system, and we also obtain the covariance matrix of the random variables.

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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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  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

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  1. Xiaofeng Zhang
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Zhang, X. A Note on the Stationary Probability Density Function and Covariance Matrix of a Stochastic Chemostat Model with Distributed Delay. Qual. Theory Dyn. Syst. 22, 114 (2023). https://doi.org/10.1007/s12346-023-00816-w

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