The dynamic behaviors in a chemostat model with delayed nutrient recycling and periodically pulsed input are studied. By introducing new analysis technique, the sufficient and necessary conditions on the permanence and extinction of the microorganisms are obtained. Furthermore, by using the Liapunov function method, the sufficient condition on the global attractivity of the model is established...

A population dynamical model describing growth of bacteria on two substrates is analyzed. The model assumes that bacteria choose substrates in order to maximize their per capita population growth rate. For batch bacterial growth, the model predicts that as the concentration of the preferred substrate decreases there will be a time at which both substrates provide bacteria with the same fitness ...

In this paper, we consider the global stability problem for the well known delayed chemostat model introduced and studied by Freedman, So and Waltman(1989). The difficulty of studying this open problem is that this delayed system has no negative feedback in the microbial populations. By a novel way of constructing a proper Liapunov functional and explicit estimates of eventual upper and lower b...

Shewanella loihica strain PV-4 harbors both a functional denitrification (NO3 (-)→N2) and a respiratory ammonification (NO3 (-)→NH4 (+)) pathway. Batch and chemostat experiments revealed that NO2 (-) affects pathway selection and the formation of reduced products. Strain PV-4 cells grown with NO2 (-) as the sole electron acceptor produced exclusively NH4 (+). With NO3 (-) as the electron accept...

Two of the central problems in biology are determining the molecular basis of adaptive evolution and understanding how cells regulate their growth. The chemostat is a device for culturing cells that provides great utility in tackling both of these problems: it enables precise control of the selective pressure under which organisms evolve and it facilitates experimental control of cell growth ra...

Abstract Many contemporary biologists and philosophers of biology admit that selection occurs at any level the biological hierarchy which entities showing heritable variation in fitness are found, while insisting entails differential reproduction, not persistence. Those who allow persistence can be selected doubt on nonreproducing reiterated, to produce “complex adaptations.” We present here a ...

This paper develops a novel characterization of uniform input-to-state stability (UISS) in terms of vector Lyapunov functions. The motivation is coming from the problem of robust global stabilization of the chemostat and in particular from anaerobic digestion processes, which are characterized by narrow stability regions and extreme sensitivity to external perturbations, if operated under optim...

Chemostat models provide the foundation for much current research in bioengineering, ecology, and population biology [8]. In engineering, the chemostat is known as the continuous-stirred tank reactor. It is used to model the dynamics of interacting organisms in waste-water treatment plants, lakes and oceans, and in biomedical contexts. The basic mathematical model of the chemostat is a system o...

We study a chemostat model that describes competition between n microbial species for a single-limited resource based on storage. The model incorporates internal resource storage variables that serve the direct connection between species growth and external resource availability. Mathematical analysis for the global dynamics of the model is carried out by using the fluctuating method. It is sho...

We study a chemostat model that describes competition between n microbial species for a single-limited resource based on storage. The model incorporates internal resource storage variables that serve the direct connection between species growth and external resource availability. Mathematical analysis for the global dynamics of the model is carried out by using the fluctuating method. It is sho...