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Global dynamics of the chemostat with overflow metabolism

Carlos Martínez 1 Jean-Luc Gouzé 1, 2
1 BIOCORE - Biological control of artificial ecosystems
CRISAM - Inria Sophia Antipolis - Méditerranée , LOV - Laboratoire d'océanographie de Villefranche, INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Abstract : We analyze the asymptotic behavior of the periodically forced light limited Droop model, representing microalgae growth. We consider general monotone growth and uptake rate functions. Based on a conservation principle, we reduce the model to a limiting planar periodic system of differential equations. The reduced system generates a monotone dynamical system. Combining this fact with results on periodic Kolmogorov equations, we find conditions such that any solution of the reduced model approaches to a positive periodic solution. Under these conditions, if the reduced system admits only one positive periodic solution, using the theory of asymptotically periodic semiflows, we extend the results on the limiting system to the original model. Finally, based on results of monotone sub-homogeneous dynamical systems, we give conditions to determine the uniqueness of positive periodic solutions
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https://hal.inria.fr/hal-03130387
Contributor : Jean-Luc Gouzé Connect in order to contact the contributor
Submitted on : Wednesday, February 3, 2021 - 3:19:42 PM
Last modification on : Thursday, January 20, 2022 - 4:17:26 PM

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Carlos Martínez, Jean-Luc Gouzé. Global dynamics of the chemostat with overflow metabolism. Journal of Mathematical Biology, Springer Verlag (Germany), 2021, 82 (3), ⟨10.1007/s00285-021-01566-6⟩. ⟨hal-03130387⟩

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