The Rosenzweig-MacArthur (1963) criterion is a graphical criterion that has been widely used for elucidating the local stability properties of the Gause (1934) type predator-prey systems. It has not been stated whether a similar criterion holds for models with explicit resource dynamics (Kooi et al. (1998)), like the chemostat model. In this paper we use the implicit function theorem and implic...

The adaptation of the tubercle bacillus to the host environment is likely to involve a complex set of gene regulatory events and physiological switches in response to environmental signals. In order to deconstruct the physiological state of Mycobacterium tuberculosis in vivo, we used a chemostat model to study a single aspect of the organism's in vivo state, slow growth. Mycobacterium bovis BCG...

tinuous stirred tank bioreactor, was independently invented by Jacques Monod1 and by Aaron Novick and Leo Szilard,2,3 who also coined the term chemostat. Its inventors conceived that this device provided a convenient way to study a bacterial population in the steady state, letting the experimenter adjust growth rate and external parameters, such as temperature or pH level. Novick and Szilard we...

Fast growing E. coli cells, in glucose-aerobic conditions, excrete fermentation by-products such as acetate. This phenomenon is known overflow metabolism and has been observed a diverse range of microorganisms. In this paper, we study chemostat model subject to metabolism: if the substrate uptake rate (or specific growth rate) above threshold (different from zero), then secretion by-product hap...

The production of lipids by oleaginous yeast and fungi becomes more important because these lipids can be used for biodiesel production. To understand the process of lipid production better, we developed a model for growth, lipid production and lipid turnover in submerged batch fermentation. This model describes three subsequent phases: exponential growth when both a C-source and an N-source ar...

We model an age-structured population feeding on an abiotic resource by combining the Gurtin-MacCamy [Math. Biosci. 43 (1979) 199] approach with a standard chemostat model. Limit cycles arise by Hopf bifurcations at low values of the chemostat dilution rate, even for simple maternity functions for which the original Gurtin-MacCamy model has no oscillatory solutions. We find the exact location i...

Traditional models of chemostat systems looking at interactions between predator, prey and nutrients have used only a single currency, such as energy or nitrogen. In reality, growth of autotrophs and heterotrophs may be limited by various elements, e.g. carbon, nitrogen, phosphorous or iron. In this study we develop a dynamic energy budget model chemostat which has both carbon and nitrogen as c...

We study the chemostat model for one species competing for one nutrient using a Lyapunov-type analysis. We design the dilution rate function so that all solutions of the chemostat converge to a prescribed periodic solution. In terms of chemostat biology, this means that no matter what positive initial levels for the species concentration and nutrient are selected, the long-term species concentr...

We study a model of competition for resource through a chemostat-type model where species consume the common resource that is constantly supplied. We assume that the species and resources are characterized by a continuous trait. As already proved, this model, although more complicated than the usual Lotka-Volterra direct competition model, describes competitive interactions leading to concentra...