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Journal Articles Discrete and Continuous Dynamical Systems - Series B Year : 2023

Stability of the chemostat system including a linear coupling between species

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Abstract

In this paper, we consider a resource-consumer model taking into account a linear coupling between species (with constant rate). The corresponding operator is proportional to a discretization of the Laplacian in such a way that the resulting dynamical system can be viewed as a regular perturbation of the classical chemostat system. We prove the existence of a unique locally asymptotically stable steady-state for every value of the transfer-rate and every value of the dilution rate not exceeding a critical value. In addition, we give an expansion of the steady-state in terms of the transfer-rate and we prove a uniform persistence property of the dynamics related to each species. Finally, we show that this equilibrium is globally asymptotically stable for every value of the transfer-rate provided that the dilution rate is with small enough values.
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Dates and versions

hal-03843598 , version 1 (08-11-2022)

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Cite

Térence Bayen, Henri Cazenave-Lacroutz, Jérôme Coville. Stability of the chemostat system including a linear coupling between species. Discrete and Continuous Dynamical Systems - Series B, 2023, 28 (3), pp.2104-2129. ⟨10.3934/dcdsb.2022160⟩. ⟨hal-03843598⟩
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