Study of the chemostat model with non-monotonic growth under random disturbances on the removal rate - INRAE - Institut national de recherche pour l’agriculture, l’alimentation et l’environnement Access content directly
Journal Articles Mathematical Biosciences and Engineering Year : 2020

Study of the chemostat model with non-monotonic growth under random disturbances on the removal rate

Abstract

We revisit the chemostat model with Haldane growth function, here subject to bounded random disturbances on the input flow rate, as often met in biotechnological or wastewater industry. We prove existence and uniqueness of global positive solution of the random dynamics and existence of absorbing and attracting sets that are independent of the realizations of the noise. We study the long-time behavior of the random dynamics in terms of attracting sets, and provide first conditions under which biomass extinction cannot b e a voided. We prove conditions for weak and strong persistence of the microbial species and provide lower bounds for the biomass concentration, as a relevant information for practitioners. The theoretical results are illustrated with numerical simulations.
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Dates and versions

hal-02971377 , version 1 (19-10-2020)

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Tomas Caraballo, Renato Colucci, Javier Lopez de La Cruz, Alain Rapaport. Study of the chemostat model with non-monotonic growth under random disturbances on the removal rate. Mathematical Biosciences and Engineering, 2020, 17 (6), pp.7480-7501. ⟨10.3934/mbe.2020382⟩. ⟨hal-02971377⟩
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