Modeling and analysis of random and stochastic input flows in the chemostat model

Abstract : In this paper we study a new way to model noisy input flows in the chemostat model, based on the Ornstein-Uhlenbeck process. We introduce a parameter β as drift in the Langevin equation, that allows to bridge a gap between a pure Wiener process, which is a common way to model random disturbances, and no noise at all. The value of the parameter β is related to the amplitude of the deviations observed on the realizations. We show that this modeling approach is well suited to represent noise on an input variable that has to take non-negative values for almost any time.
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Tomas Caraballo, Maria-José Garrido-Atienza, Javier López-De-La-Cruz, Alain Rapaport. Modeling and analysis of random and stochastic input flows in the chemostat model. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2019, 24 (8), pp.3591-3614. ⟨http://aimsciences.org//article/doi/10.3934/dcdsb.2018280⟩. ⟨10.3934/dcdsb.2018280⟩. ⟨hal-01819374⟩

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