A chemostat model of a single species feeding on a limiting nutrient supplied at a constant rate is proposed. The model incorporates a general nutrient uptake function and a distributed delay. The delay indicates that the growth of the species depends on the past concentration of nutrient. Using the average time delay as a bifurcation parameter, it is proven that the model undergoes a sequence ...

A model of competition for two complementary nutrients between plasmid-bearing and plasmid-free organisms in a chemostat is proposed. A rigorous mathematical analysis of the global asymptotic behavior of the model is presented. The work extends the model of competition for a single-limited nutrient studied by Stephanopoulos and Lapidus [Chem. Engng. Sci. 443 (1988) 49] and Hsu, Waltman and Wolk...

A model of two species consuming a single, limited, periodically added resource is discussed. The model is based on chemostat-type equations, which differ from the classical models of Lotka and Volterra. The model incorporates nonlinear 'functional response' curves of the Holling or Michaelis-Menten type to describe the dependence of the resource-exploitation rate on the amount of resource. Coe...

The objective of this study was to optimize continuous acetone-butanol-ethanol (ABE) fermentation using a two stage chemostat system integrated with liquid-liquid extraction of solvents produced in the first stage. This minimized end product inhibition by butanol and subsequently enhanced glucose utilization and solvent production in continuous cultures of Clostridium acetobutylicum B 5313. Dur...

In a chemostat, transient oscillations in cell number density are often experimentally observed during cell growth. The aim of this paper is to propose a simple autonomous model which is able to generate these oscillations, and to investigate it analytically. Our point of view is based on a simplification of the cell cycle in which there are two states (mature and immature) with the transfer be...

The aim of this paper is to study the dynamics of predator-prey interaction in a chemostat to determine whether including a discrete delay to model the time between the capture of the prey and its conversion to viable biomass can introduce oscillatory dynamics even though there is a globally asymptotically stable equilibrium when the delay is ignored. Hence, Holling type I response functions ar...

This paper studies the global asymptotic behavior of an exploitative competition model between n species in a chemostat. The model incorporates discrete time delays to describe the delay in the conversion of nutrient consumed to viable biomass and hence includes delays simultaneously in variables of nutrient and species concentrations. In the case where only two species are engaged in competiti...

We are interested in modeling the Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions, in the specific scales of the biological framework of adaptive dynamics. Adaptive dynamics so far has been put on a rigorous footing only for direct competition models (Lotka-Volterra models) involving a competition kernel which descri...