Operating diagrams for a three-tiered microbial food web in the chemostat.

In this paper, we consider a three-tiered food web model in a chemostat, including chlorophenol, phenol, and hydrogen substrates and their degraders. The model takes into account the three substrate inflowing concentrations, as well as maintenance, that is, decay terms of the species. The operating diagrams give the asymptotic behavior of the model with respect to the four operating parameters, which are the dilution rate and the three inflowing concentrations of the substrates.

Sensitivity analysis and reduction of a dynamic model of a bioproduction of fructo-oligosaccharides.

Starting from a relatively detailed model of a bioprocess producing fructo-oligosaccharides, a set of experimental data collected in batch and fed-batch experiments is exploited to estimate the unknown model parameters. The original model includes the growth of the fungus Aureobasidium pullulans which produces the enzymes responsible for the hydrolysis and transfructosylation reactions, and as such contains 25 kinetic parameters and 16 pseudo-stoichiometric coefficients, which are not uniquely identifiable with the data at hand. The aim of this study is, therefore, to show how sensitivity analysis and quantitative indicators based on the Fisher information matrix can be used to reduce the detailed model to a practically identifiable model.

A density-dependent model of competition for one resource in the chemostat.

This paper deals with a two-microbial species model in competition for a single-resource in the chemostat including general intra- and interspecific density-dependent growth rates with distinct removal rates for each species. In order to understand the effects of intra- and interspecific interference, this general model is first studied by determining the conditions of existence and local stability of steady states. With the same removal rate, the model can be reduced to a planar system and then the global stability results for each steady state are derived.

Competition for a single resource and coexistence of several species in the chemostat.

We study a model of the chemostat with several species in competition for a single resource. We take into account the intra-specific interactions between individuals of the same population of micro-organisms and we assume that the growth rates are increasing and the dilution rates are distinct. Using the concept of steady-state characteristics, we present a geometric characterization of the existence and stability of all equilibria.