Effects of spatial structure and diffusion on the performances of the chemostat

Ihab Haidar; Alain Rapaport; Frédéric Gérard; Ihab Haidar; Alain Rapaport; Frédéric Gérard

doi:10.3934/mbe.2011.8.953

Mathematical Biosciences and Engineering

2011, Volume 8, Issue 4: 953-971. doi: 10.3934/mbe.2011.8.953

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Effects of spatial structure and diffusion on the performances of the chemostat

1.
UMR INRA/SupAgro 'MISTEA' and EPI INRA/INRIA 'MODEMIC', 2, pl. Viala 34060, Montpellier
2.
UMR Analyse des Systèmes et Biométrie, INRA, EPI INRA/INRIA 'MODEMIC', 2 pl. Viala 34060 Montpellier
3.
UMR INRA/SupAgro/CIRAD/IRD 'Eco&Sols', 2, pl. Viala 34060, Montpellier

Received: 01 November 2010 Accepted: 29 June 2018 Published: 01 August 2011
MSC : Primary: 34D05, 34D23; Secondary: 92D25.

Given hydric capacity and nutrient flow of a chemostat-like system, we analyse the influence of a spatial structure on the output concentrations at steady-state. Three configurations are compared: perfectly-mixed, serial and parallel with diffusion rate. We show the existence of a threshold on the input concentration of nutrient for which the benefits of the serial and parallel configurations over the perfectly-mixed one are reversed. In addition, we show that the dependency of the output concentrations on the diffusion rate can be non-monotonic, and give precise conditions for the diffusion effect to be advantageous. The study encompasses dead-zone models.
- global stability.,
- Chemostat model,
- interconnection,
- diffusion
Citation: Ihab Haidar, Alain Rapaport, Frédéric Gérard. Effects of spatial structure and diffusion on the performances of the chemostat[J]. Mathematical Biosciences and Engineering, 2011, 8(4): 953-971. doi: 10.3934/mbe.2011.8.953

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Abstract

Given hydric capacity and nutrient flow of a chemostat-like system, we analyse the influence of a spatial structure on the output concentrations at steady-state. Three configurations are compared: perfectly-mixed, serial and parallel with diffusion rate. We show the existence of a threshold on the input concentration of nutrient for which the benefits of the serial and parallel configurations over the perfectly-mixed one are reversed. In addition, we show that the dependency of the output concentrations on the diffusion rate can be non-monotonic, and give precise conditions for the diffusion effect to be advantageous. The study encompasses dead-zone models.
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