Long-time analysis of a stochastic chemostat model with instantaneous nutrient recycling

Xiaoxia Guo; Dehao Ruan; Xiaoxia Guo; Dehao Ruan

doi:10.3934/math.2023469

AIMS Mathematics

2023, Volume 8, Issue 4: 9331-9351. doi: 10.3934/math.2023469

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Long-time analysis of a stochastic chemostat model with instantaneous nutrient recycling

Xiaoxia Guo ¹,
Dehao Ruan ^{2
,
,}

1.
School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, Shanxi, 030006, China
2.
School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou, Guangdong, 510665, China

Received: 02 September 2022 Revised: 30 November 2022 Accepted: 07 December 2022 Published: 15 February 2023
MSC : 34F05, 37H10, 60H10

This paper presents long-time analysis of a stochastic chemostat model with instantaneous nutrient recycling. We focus on the investigation of the sufficient and almost necessary conditions of the exponential extinction and persistence for the model. The convergence to the invariant measure is also established under total variation norm. Our work generalizes and improves many existing results. One of the interesting findings is that random disturbance can suppress microorganism growth, which can provide us some useful control strategies to microbiological cultivation. Finally, some numerical simulations partly based on the stochastic sensitive function technique are given to illustrate theoretical results.
- stochastic chemostat model,
- extinction,
- persistence,
- ergodicity
Citation: Xiaoxia Guo, Dehao Ruan. Long-time analysis of a stochastic chemostat model with instantaneous nutrient recycling[J]. AIMS Mathematics, 2023, 8(4): 9331-9351. doi: 10.3934/math.2023469

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Abstract

This paper presents long-time analysis of a stochastic chemostat model with instantaneous nutrient recycling. We focus on the investigation of the sufficient and almost necessary conditions of the exponential extinction and persistence for the model. The convergence to the invariant measure is also established under total variation norm. Our work generalizes and improves many existing results. One of the interesting findings is that random disturbance can suppress microorganism growth, which can provide us some useful control strategies to microbiological cultivation. Finally, some numerical simulations partly based on the stochastic sensitive function technique are given to illustrate theoretical results.

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