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Approximation of the Fokker–Planck equation of the stochastic chemostat

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  • Campillo, Fabien
  • Joannides, Marc
  • Larramendy-Valverde, Irène

Abstract

We consider a stochastic model of the two-dimensional chemostat as a diffusion process for the concentration of substrate and the concentration of biomass. The model allows for the washout phenomenon: the disappearance of the biomass inside the chemostat. We establish the Fokker–Planck equation associated with this diffusion process, in particular we describe the boundary conditions that modelize the washout. We propose an adapted finite difference scheme for the approximation of the solution of the Fokker–Planck equation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:99:y:2014:i:c:p:37-53
    DOI: 10.1016/j.matcom.2013.04.012
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    References listed on IDEAS

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    1. Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
    2. Campillo, F. & Joannides, M. & Larramendy-Valverde, I., 2011. "Stochastic modeling of the chemostat," Ecological Modelling, Elsevier, vol. 222(15), pages 2676-2689.
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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).

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