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A stochastic chemostat model with mean-reverting Ornstein-Uhlenbeck process and Monod-Haldane response function

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  • Zhang, Xiaofeng
  • Yuan, Rong

Abstract

In this paper, we mainly construct and analyze a stochastic chemostat model with mean-reverting Ornstein-Uhlenbeck process and Monod-Haldane response function, which is a stochastic non-autonomous system. We first study the existence of global unique positive solution with any initial value for stochastic chemostat system. After that, the sufficient conditions are established for extinction exponentially and persistence in the mean of microorganism. Finally, we also give numerical simulations to illustrate our main conclusions. Our results show that the mean-reverting process is an effective and reasonable method to introduce environmental noise into the continuous culture model of microorganism, and we also find that the reversion speed and volatility intensity have an important influence on the extinction and persistence of microorganism.

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  • Zhang, Xiaofeng & Yuan, Rong, 2021. "A stochastic chemostat model with mean-reverting Ornstein-Uhlenbeck process and Monod-Haldane response function," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    • Handle: RePEc:eee:apmaco:v:394:y:2021:i:c:s0096300320307864
    DOI: 10.1016/j.amc.2020.125833
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    References listed on IDEAS

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    1. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    2. Sun, Shulin & Zhang, Xiaolu, 2018. "A stochastic chemostat model with an inhibitor and noise independent of population sizes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1763-1781.
    3. Yan, Rong & Sun, Shulin, 2020. "Stochastic characteristics of a chemostat model with variable yield," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    4. Rong Yan & Shulin Sun, 2020. "Stochastic Characteristics and Optimal Control for a Stochastic Chemostat Model with Variable Yield," Complexity, Hindawi, vol. 2020, pages 1-18, April.
    5. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
    6. Sun, Shulin & Zhang, Xiaofeng, 2018. "Asymptotic behavior of a stochastic delayed chemostat model with nonmonotone uptake function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 38-56.
    7. Campillo, F. & Joannides, M. & Larramendy-Valverde, I., 2011. "Stochastic modeling of the chemostat," Ecological Modelling, Elsevier, vol. 222(15), pages 2676-2689.
    8. Sun, Shulin & Sun, Yaru & Zhang, Guang & Liu, Xinzhi, 2017. "Dynamical behavior of a stochastic two-species Monod competition chemostat model," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 153-170.
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