A model of two microbial species in a chemostat competing for single resource the presence an internal inhibitor is considered. The four-dimensional system ordinary differential equations. Using general growth rate functions species, we give complete analysis existence and local stability all steady states. We describe behavior with respect to operating parameters represented by dilution input ...

We study a class of size-structured, ODE models of growth in the chemostat, that take into account cell maintenance and substrate dependent cell mortality. Unlike most classical chemostat models, they are supposed to be non-conservative, in the sense that they do not verify the mass conservation principle. However, using a change of time scale, we are able to obtain qualitative results. Then, u...

In this paper, we consider a competition model between n species in a chemostat including both monotone and non-monotone response functions, distinct removal rates and variable yields. We show that only the species with the lowest break-even concentration survives, provided that additional technical conditions on the growth functions and yields are satisfied. LaSalle’s extension theorem of the ...

This paper deals with the problem of selective harvesting in a chemostat model. Here, we have taken the purifying effort as a dynamic variable and tax as a control instrument. The existence of the possible steady states along with their globally stable equilibrium is discussed. The optimal tax policy is also discussed with the help of Pontryagin’s maximum principle. Finally, numerical examples ...

Abstract. In this paper, we consider a basic N-dimensional competition model in the unstirred chemostat with Beddington-DeAngelis functional response. The bifurcation solutions from a simple eigenvalue and a double eigenvalue are obtained respectively. In particular, for the double eigenvalue, we establish the existence and stability of coexistence solutions by the techniques of space decomposi...

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 mathematic...

two different growth media, namely complex and defined media, were used to examine establishment of steady-state conditions in phosphate-limited culture system of saccharomyces cerevisiae cen.pk113-5d strain. using the defined growth medium, it was possible to obtain steady state condition in the continuous culture. the effect of phosphate concentration on the growth of s. cerevisiae in phospha...

A two-stage chemostat was used to study removal of cadmium by microorganisms in continuous culture. The medium was contaminated with 0.8 mg of Cd per liter. At 20 degrees C, most of the microbial biomass formed aggregates which settled in the second stage of the chemostat. Effluent was free of bacteria. Up to 80% of the metal contained in the inlet flux was removed by the biomass, with 20% rema...