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Long-Time Behavior and Density Function of a Stochastic Chemostat Model with Degenerate Diffusion

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Abstract

This paper considers a stochastic chemostat model with degenerate diffusion. Firstly, the Markov semigroup theory is used to establish sufficient criteria for the existence of a unique stable stationary distribution. The authors show that the densities of the distributions of the solutions can converge in L1 to an invariant density. Then, conditions are obtained to guarantee the washout of the microorganism. Furthermore, through solving the corresponding Fokker-Planck equation, the authors give the exact expression of density function around the positive equilibrium of deterministic system. Finally, numerical simulations are performed to illustrate the theoretical results.

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Author information

Authors and Affiliations

  1. College of Science, China University of Petroleum (East China), Qingdao, 266580, China

    Miaomiao Gao & Daqing Jiang

  2. Key Laboratory of Unconventional Oil and Gas Development, China University of Petroleum (East China), Ministry of Education, Qingdao, 266580, China

    Daqing Jiang

  3. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Daqing Jiang

  4. Department of Mathematics, Yanbian University, Yanji, 133002, China

    Xiangdan Wen

Authors
  1. Miaomiao Gao
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  2. Daqing Jiang
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  3. Xiangdan Wen
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Corresponding author

Correspondence to Xiangdan Wen.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 11871473, the Natural Science Foundation of Shandong Province under Grant No. ZR2019MA010 and the Science and Technology Research Project of Jilin Provincial Department of Education of China under Grant No. JJKH20180462KJ.

This paper was recommended for publication by Editor LIU Shujun.

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Gao, M., Jiang, D. & Wen, X. Long-Time Behavior and Density Function of a Stochastic Chemostat Model with Degenerate Diffusion. J Syst Sci Complex 35, 931–952 (2022). https://doi.org/10.1007/s11424-021-0170-9

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  • DOI: https://doi.org/10.1007/s11424-021-0170-9

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