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Journal Articles Nonlinear Analysis: Real World Applications Year : 2012

Global stability for a model of competition in the chemostat with microbial inputs

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Abstract

We propose a model of competition of nn species in a chemostat, with constant input of some species. We mainly emphasize the case that can lead to coexistence in the chemostat in a non-trivial way, i.e., where the n−1n−1 less competitive species are in the input. We prove that if the inputs satisfy a constraint, the coexistence between the species is obtained in the form of a globally asymptotically stable (GAS) positive equilibrium, while a GAS equilibrium without the dominant species is achieved if the constraint is not satisfied. This work is round up with a thorough study of all the situations that can arise when having an arbitrary number of species in the chemostat inputs; this always results in a GAS equilibrium that either does or does not encompass one of the species that is not present in the input.
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Dates and versions

hal-00848445 , version 1 (26-07-2013)

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Gonzalo Robledo, Frédéric Grognard, Jean-Luc Gouzé. Global stability for a model of competition in the chemostat with microbial inputs. Nonlinear Analysis: Real World Applications, 2012, 13 (2), pp.582-598. ⟨10.1016/j.nonrwa.2011.07.049⟩. ⟨hal-00848445⟩
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