Statistical property analysis for a stochastic chemostat model with degenerate diffusion

Jingen Yang; Zhong Zhao; Xinyu Song; Jingen Yang; Zhong Zhao; Xinyu Song

doi:10.3934/math.2023090

AIMS Mathematics

2023, Volume 8, Issue 1: 1757-1769. doi: 10.3934/math.2023090

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Research article

Statistical property analysis for a stochastic chemostat model with degenerate diffusion

1.
School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China
2.
School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China

Received: 19 August 2022 Revised: 11 October 2022 Accepted: 13 October 2022 Published: 24 October 2022
MSC : 92B05, 60H10

By considering the fact that the growth of microorganisms in a chemostat is subject to white noise, we construct a stochastic chemostat model with degenerate diffusion by using a discrete Markov chain. By solving the corresponding Fokker-Planck equation, we derive the explicit expression of the stationary joint probability density, which peaks near the deterministic equilibrium. Next, we simulate the the marginal probability density functions for different noise intensities and further discuss the relationship of the marginal probability density function and noise intensities. For the statistical properties of the stochastic model, we mainly investigate the effect of white noise on the variance and skewness of the concentration of microorganisms.
- stochastic chemostat model,
- degenerate diffusion,
- stationary probability density,
- statistical property
Citation: Jingen Yang, Zhong Zhao, Xinyu Song. Statistical property analysis for a stochastic chemostat model with degenerate diffusion[J]. AIMS Mathematics, 2023, 8(1): 1757-1769. doi: 10.3934/math.2023090

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Abstract

By considering the fact that the growth of microorganisms in a chemostat is subject to white noise, we construct a stochastic chemostat model with degenerate diffusion by using a discrete Markov chain. By solving the corresponding Fokker-Planck equation, we derive the explicit expression of the stationary joint probability density, which peaks near the deterministic equilibrium. Next, we simulate the the marginal probability density functions for different noise intensities and further discuss the relationship of the marginal probability density function and noise intensities. For the statistical properties of the stochastic model, we mainly investigate the effect of white noise on the variance and skewness of the concentration of microorganisms.

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