IDEAS home Printed from https://ideas.repec.org/a/eee/ecomod/v222y2011i15p2676-2689.html
   My bibliography  Save this article

Stochastic modeling of the chemostat

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304380011002572
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ecolmodel.2011.04.027?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. 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.
    3. 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).
    4. 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.
    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. 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.
    7. Zhang, Xiaofeng & Yuan, Rong, 2021. "Forward attractor for stochastic chemostat model with multiplicative noise," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    8. 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).
    9. 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.
    10. 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.
    11. Fritsch, Coralie & Harmand, Jérôme & Campillo, Fabien, 2015. "A modeling approach of the chemostat," Ecological Modelling, Elsevier, vol. 299(C), pages 1-13.
    12. 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.
    13. 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.
    14. 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).
    15. 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).
    16. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Christian H. Weiß & Philip K. Pollett, 2012. "Chain Binomial Models and Binomial Autoregressive Processes," Biometrics, The International Biometric Society, vol. 68(3), pages 815-824, September.
    2. Artalejo, J.R. & Lopez-Herrero, M.J., 2011. "The SIS and SIR stochastic epidemic models: A maximum entropy approach," Theoretical Population Biology, Elsevier, vol. 80(4), pages 256-264.
    3. Ross, J.V., 2012. "On parameter estimation in population models III: Time-inhomogeneous processes and observation error," Theoretical Population Biology, Elsevier, vol. 82(1), pages 1-17.
    4. Jonathan Fintzi & Jon Wakefield & Vladimir N. Minin, 2022. "A linear noise approximation for stochastic epidemic models fit to partially observed incidence counts," Biometrics, The International Biometric Society, vol. 78(4), pages 1530-1541, December.
    5. Keeling, M.J. & Ross, J.V., 2009. "Efficient methods for studying stochastic disease and population dynamics," Theoretical Population Biology, Elsevier, vol. 75(2), pages 133-141.
    6. Rebuli, Nicolas P. & Bean, N.G. & Ross, J.V., 2018. "Estimating the basic reproductive number during the early stages of an emerging epidemic," Theoretical Population Biology, Elsevier, vol. 119(C), pages 26-36.
    7. Gamboa, M. & López-García, M. & Lopez-Herrero, M.J., 2024. "On the exact and population bi-dimensional reproduction numbers in a stochastic SVIR model with imperfect vaccine," Applied Mathematics and Computation, Elsevier, vol. 468(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecomod:v:222:y:2011:i:15:p:2676-2689. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/ecological-modelling .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.