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Stochastic characteristics of a chemostat model with variable yield

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  • Yan, Rong
  • Sun, Shulin

Abstract

In this paper, a stochastic chemostat model with variable yield is investigated. The environment noises are given by independent standard Brownian motions, and the yield coefficient reflecting the conversion of nutrient to microorganism varies depending on the ambient nutrient. First, we give that the stochastic system has a unique global positive solution. Second, the sufficient conditions for the extinction and strong persistence in the mean of the microorganism are established. Third, by using stochastic Lyapunov function, the existence of a unique stationary distribution to the stochastic model is studied. In addition, some numerical simulations are carried to illustrate the theoretical results and the influence of the variable yield on the microorganism.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:537:y:2020:i:c:s0378437119315298
    DOI: 10.1016/j.physa.2019.122681
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    References listed on IDEAS

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    1. 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.
    2. Campillo, F. & Joannides, M. & Larramendy-Valverde, I., 2011. "Stochastic modeling of the chemostat," Ecological Modelling, Elsevier, vol. 222(15), pages 2676-2689.
    3. Fu, Guifang & Ma, Wanbiao, 2006. "Hopf bifurcations of a variable yield chemostat model with inhibitory exponential substrate uptake," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 845-850.
    4. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2018. "Stationary distribution and extinction of a stochastic predator–prey model with additional food and nonlinear perturbation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 226-239.
    5. 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.
    6. 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.
    7. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Stationary distribution and extinction of a stochastic HIV-1 model with Beddington–DeAngelis infection rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 414-426.
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    Cited by:

    1. Zhang, Xiaofeng & Yuan, Rong, 2021. "Forward attractor for stochastic chemostat model with multiplicative noise," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    2. 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).

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