The asymptotic behavior of a tri-trophic food chain model in the chemostat is studied. The Monod-Herbert growth model is used for all trophic levels. The analysis is carried out numerically, by finding both local and global bifurcations of equilibria and of limit cycles with respect to two chemostat control parameters: the dilution rate of the chemostat and the concentration of input substrate....

The chemostat plays a well-established role as a model open system in ecology the comprehensive monograph see [HSm95]. Basically, the chemostat consists of a nutrient input pumped at a constant rate into a well-mixed culture vessel. Volume is kept constant by pumping the mixed contents out at the same rate. We assume all nutrients needed for growth, except one, to be present in abundance. In ad...

We present bounded dynamic (but observer-free) output feedback laws that achieve global stabilization of equilibrium profiles of the partial differential equation (PDE) model of a simplified, age-structured chemostat model. The chemostat PDE state is positive-valued, which means that our global stabilization is established in the positive orthant of a particular function space—a rather non-stan...

In this work, we study a model of the chemostat where the species are present in two forms, isolated and aggregated individuals, such as attached bacteria or bacteria in flocks. We show that our general model contains a lot of models that were previously considered in the literature. Assuming that flocculation and deflocculation dynamics are fast compared to the growth of the species, we constr...

Lipid-accumulating fungi may be able to produce biodiesel precursors from agricultural wastes. As a first step in understanding and evaluating their potential, a mathematical model was developed to describe growth, lipid accumulation and substrate consumption of the oleaginous fungus Umbelopsis isabellina (also known as Mortierella isabellina) in submerged chemostat cultures. Key points of the ...

We consider a stochastic model of the two-dimensional chemostat as a diffusion process for the concentration of substrate and the concentration of biomass. The model allows for the washout phenomenon: the disappearance of the biomass inside the chemostat. We establish the Fokker-Planck associated with this diffusion process, in particular we describe the boundary conditions that modelize the wa...

A chemostat model with delayed response in growth and impulsive diffusion and input on nutrients is considered. Using the discrete dynamical system determined by the stroboscopic map, we obtain a microorganism-extinction periodic solution. Further, it is globally attractive. The permanent condition of the investigated system is also obtained by the theory on impulsive delay differential equatio...