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Stochastic modeling of the chemostat

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  • Campillo, F.
  • Joannides, M.
  • Larramendy-Valverde, I.

Abstract

The chemostat is classically represented, at large population scale, as a system of ordinary differential equations. Our goal is to establish a set of stochastic models that are valid at different scales: from the small population scale to the scale immediately preceding the one corresponding to the deterministic model. At a microscopic scale we present a pure jump stochastic model that gives rise, at the macroscopic scale, to the ordinary differential equation model. At an intermediate scale, an approximation diffusion allows us to propose a model in the form of a system of stochastic differential equations. We expound the mechanism to switch from one model to another, together with the associated simulation procedures. We also describe the domain of validity of the different models.

Suggested Citation

  • Campillo, F. & Joannides, M. & Larramendy-Valverde, I., 2011. "Stochastic modeling of the chemostat," Ecological Modelling, Elsevier, vol. 222(15), pages 2676-2689.
    • Handle: RePEc:eee:ecomod:v:222:y:2011:i:15:p:2676-2689
    DOI: 10.1016/j.ecolmodel.2011.04.027
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    References listed on IDEAS

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    1. Ross, J.V. & Pagendam, D.E. & Pollett, P.K., 2009. "On parameter estimation in population models II: Multi-dimensional processes and transient dynamics," Theoretical Population Biology, Elsevier, vol. 75(2), pages 123-132.
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    Cited by:

    1. 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.
    2. Wang, Liang & Jiang, Daqing, 2017. "Periodic solution for the stochastic chemostat with general response function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 378-385.
    3. Fritsch, Coralie & Harmand, Jérôme & Campillo, Fabien, 2015. "A modeling approach of the chemostat," Ecological Modelling, Elsevier, vol. 299(C), pages 1-13.
    4. Lifan Chen & Xingwang Yu & Sanling Yuan, 2022. "Effects of Random Environmental Perturbation on the Dynamics of a Nutrient–Phytoplankton–Zooplankton Model with Nutrient Recycling," Mathematics, MDPI, vol. 10(20), pages 1-23, October.
    5. 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).
    6. Fabien Campillo & Marc Joannides & Irène Larramendy-Valverde, 2016. "Analysis and Approximation of a Stochastic Growth Model with Extinction," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 499-515, June.
    7. Wang, Liang & Jiang, Daqing & Feng, Tao, 2022. "Threshold dynamics in a stochastic chemostat model under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    8. Yu Mu & Zuxiong Li & Huili Xiang & Hailing Wang, 2019. "Dynamical Analysis of a Stochastic Multispecies Turbidostat Model," Complexity, Hindawi, vol. 2019, pages 1-18, January.
    9. Zhang, Xiaofeng & Yuan, Rong, 2021. "Forward attractor for stochastic chemostat model with multiplicative noise," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    10. Cao, Zhongwei & Wen, Xiangdan & Su, Huishuang & Liu, Liya & Ma, Qiang, 2020. "Stationary distribution of a stochastic chemostat model with Beddington–DeAngelis functional response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    11. Xu, Chaoqun & Yuan, Sanling & Zhang, Tonghua, 2018. "Sensitivity analysis and feedback control of noise-induced extinction for competition chemostat model with mutualism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 891-902.
    12. Campillo, Fabien & Joannides, Marc & Larramendy-Valverde, Irène, 2014. "Approximation of the Fokker–Planck equation of the stochastic chemostat," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 99(C), pages 37-53.
    13. 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.
    14. Zhao, Dianli & Yuan, Sanling, 2018. "Sharp conditions for the existence of a stationary distribution in one classical stochastic chemostat," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 199-205.
    15. 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).
    16. Liu, Rong & Ma, Wanbiao, 2021. "Noise-induced stochastic transition: A stochastic chemostat model with two complementary nutrients and flocculation effect," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

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