Pré-Publication, Document De Travail Année : 2025

Global stability of perturbed chemostat systems

Résumé

This paper is devoted to the analysis of global stability of the chemostat system with a perturbation term representing any type of exchange between species. This conversion term depends on species and substrate concentrations but also on a positive perturbation parameter. After having written the invariant manifold as a union of a family of compact subsets, our main result states that for each subset in this family, there is a positive threshold for the perturbation parameter below which, the system is globally asymptotically stable in the corresponding subset. Our approach relies on the Malkin-Gorshin Theorem and on a Theorem by Smith and Waltman about perturbations of a globally stable steady state. Properties of steady-states and numerical simulations of the system's asymptotic behavior complete this study for two types of perturbation term between species.

système chemostat, systèmes dynamiques, perturbations, stabilité
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Dates et versions

hal-04860652 , version 1 (01-01-2025)
hal-04860652 , version 2 (14-01-2025)

Identifiants

  • HAL Id : hal-04860652 , version 2

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C Alvarez-Latuz, T Bayen, J Coville. Global stability of perturbed chemostat systems. 2025. ⟨hal-04860652v2⟩
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