‎In this paper‎, ‎the fractional--order form of three dimensional chemostat model with variable yields is introduced‎. ‎The stability analysis of this fractional system is discussed in detail‎. ‎In order to study the dynamic behaviours of the mentioned fractional system‎, ‎the well known nonstandard (NSFD) scheme is implemented‎. ‎The proposed NSFD scheme is compared with the forward Euler and ...

This paper discusses a model of two interconnected chemostats in series, characterized by biomass mortality. A comparison is established with single chemostat the same total volume different cases, that are or without mortality rate. The outlet substrate concentration and biogas flow rate main criteria for comparison. According to conditions depending on operating parameters distribution volume...

The aim of this course is to describe the mathematical model of competition in the chemostat and to study various mechanisms of coexistence of species. Basically, the chemostat consists of a nutrient input, pumped at a constant rate into a well-mixed culture vessel. The culture vessel contains the microorganisms that are growing and competing for the nutrient. Volume is kept constant by pumping...

A model of the simple chemostat which allows for growth on the wall (or other marked surface) is presented as three nonlinear ordinary differential equations. The organisms which are attached to the wall do not wash out of the chemostat. This destroys the basic reduction of the chemostat equations to a monotone system, a technique which has been useful in the analysis of many chemostat-like equ...

The influence of dilution rate on the production of biomass, ethanol, and invertase in an aerobic culture of Succharornyces carlsbergensis was studied in a glucoselimited chemostat culture. A kinetic model was developed to analyze the biphasic growth of yeast on both the glucose remaining and the ethanol produced in the culture. The model assumes a double effect where glucose regulates the flux...

A discrete, size-structured model of phytoplankton growth in the chemostat. A discrete, size-structured model of phytoplankton growth in the chemostat. Abstract: We introduce inhomogeneous, substrate dependent cell division in a nonlinear matrix model of size-structured population growth in the chemostat, rst introduced by Gage et al. 7] and later analyzed by Smith 11]. We show that mass conser...

This paper deals with an almost-global stability result for a particular chemostat model. It deviates from the classical chemostat because crowding effects are taken into consideration. This model can be rewritten as a negative feedback interconnection of two systems which are monotone (as input-output systems). Moreover, these subsystems behave nicely when subject to constant inputs. This allo...

We consider the modeling of the dynamics of the chemostat at its very source. The chemostat is classically represented as a system of ordinary differential equations. Our goal is to establish a stochastic model that is valid at the scale immediately preceding the one corresponding to the deterministic model. At a microscopic scale we present a pure jump stochastic model that gives rise, at the ...

We consider the modeling of the dynamics of the chemostat at its very source. The chemostat is classically represented as a system of ordinary differential equations. Our goal is to establish a stochastic model that is valid at the scale immediately preceding the one corresponding to the deterministic model. At a microscopic scale we present a pure jump stochastic model that gives rise, at the ...

A discrete-delayed model of plasmid-bearing, plasmid-free organisms competing for a single-limited nutrient in a chemostat is established. Rigorous mathematical analysis of the asymptotic behavior of this model is presented. An interesting method to analyze the local stability of interior equilibrium is developed. The argument is also applicable to a model of plasmidbearing, plasmid-free organi...