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

Authors
Journal
Nonlinear Analysis Real World Applications
1468-1218
Publisher
Elsevier
Volume
13
Issue
2
Identifiers
DOI: 10.1016/j.nonrwa.2011.07.049
Keywords
  • Competitive Exclusion
  • Global Stability
  • Chemostat
  • Polytopic Lyapunov Functions

Abstract

We propose a model of competition of n 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−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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