The buffered chemostat with non-monotonic response functions

We study how a particular spatial structure with a buffer impacts the number of equilibria and their stability in the chemostat model. We show that the occurrence of a buffer can allow a species to persist or on the opposite to go extinct, depending on the characteristics of the buffer. For non-monotonic response functions, we characterize the buffered configurations that make the chemostat dynamics globally asymptotically stable, while this is not possible with single, serial or parallel vessels of the same total volume and input flow. These results are illustrated with the Haldane kinetic function.Comment: 9th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2013), Toulouse : France (2013

A modeling approach of the chemostat

Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit this approach by complementing these classic formalisms by stochastic formalisms and to explain the links between these representations in terms of mathematical analysis but also in terms of modeling and numerical simulations. We illustrate this approach on the model of chemostat.Comment: arXiv admin note: substantial text overlap with arXiv:1308.241

Minimal-time bioremediation of natural water resources

We study minimal time strategies for the treatment of pollution of large volumes, such as lakes or natural reservoirs, with the help of an autonomous bioreactor. The control consists in feeding the bioreactor from the resource, the clean output returning to the resource with the same flow rate. We first characterize the optimal policies among constant and feedback controls, under the assumption of a uniform concentration in the resource. In a second part, we study the influence of an inhomogeneity in the resource, considering two measurements points. With the help of the Maximum Principle, we show that the optimal control law is non-monotonic and terminates with a constant phase, contrary to the homogeneous case for which the optimal flow rate is decreasing with time. This study allows the decision makers to identify situations for which the benefit of using non-constant flow rates is significant

About overyielding with mixed cultures in batch processes

International audienceThis paper investigates-via modeling-several possible explanations of overyielding observed in mixed cultures cultivated in batch reactors. It is first shown that the classical model of competition of N species for a single resource cannot explain such overyielding. Then, three hypotheses are introduced and discussed at the light of numerical simulations

Global stabilization of the chemostat with delayed and sampled measurements and control

International audienceThe classical model of the chemostat with one substrate, one species and a Haldane type growth rate function is considered. The input substrate concentration is supposed to be constant and the dilution rate is considered as the control. The problem of asymptotically stabilizing an equilibrium point of this system in the case where the measured concentrations are delayed and piecewise constant with a piecewise constant control is addressed

Contrôle de paramètres dans un chémostat

International audienc

Analysis of a mathematical model of syntrophic bacteria in a chemostat

A mathematical model involving a syntrophic relationship between two populations of bacteria in a continuous culture is proposed. A detailed qualitative analysis is carried out. The local and global stability analysis of the equilibria are performed. We demonstrate, under general assumptions of monotonicity, relevant from an applied point of view, the asymptotic stability of the positive equilibrium point which corresponds to the coexistence of the two bacteria. A syntrophic relationship in the anaerobic digestion process is proposed as a real candidate for this model

About biomass overyielding of mixed cultures in batch processes

International audienceWe study mechanisms that can produce an increase of biomass production in batch processes when considering mixed cultures, compared to pure cultures. We show that growth thresholds or variable yields can produce 'overyielding', while this is not possible in the classical batch model with multiple species. We give sufficient conditions on the characteristics of the species to obtain overyielding, and illustrate these theoretical results with numerical simulations. This work provides new insights on species complementary in models of mixed cultures, without having to consider direct interactions terms between species as, for instance in the well known Generalized Lotka-Volterra model

About biomass overyielding of mixed cultures in batch processes

We study mechanisms that can produce an increase of biomass production in batch processes when considering mixed cultures, compared to pure cultures. We show that growth thresholds or variable yields can produce 'overyielding', while this is not possible in the classical batch model with multiple species. We give sufficient conditions on the characteristics of the species to obtain overyielding, and illustrate these theoretical results with numerical simulations. This work provides new insights on species complementary in models of mixed cultures, without having to consider direct interactions terms between species as, for instance in the well known Generalized Lotka-Volterra model