# The Simple Chemostat with Wall Growth

```@article{Pilyugin1999TheSC,
title={The Simple Chemostat with Wall Growth},
author={Sergei S. Pilyugin and Paul Waltman},
journal={SIAM J. Appl. Math.},
year={1999},
volume={59},
pages={1552-1572}
}```
• Published 1 May 1999
• Mathematics
• SIAM J. Appl. Math.
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 equations. The adherence to and shearing from the wall eliminates the boundary equilibria. For a…

## Figures from this paper

• Mathematics, Economics
Taiwanese Journal of Mathematics
• 2021
In this paper, we construct a simple chemostat-based variable yield model of competition between two bacterial strains, one of which is capable of wall growth [14]. In this model we prove the
• Mathematics
• 2020
. Understanding and exploiting the ﬂocculation process is a major challenge in the mathematical theory of the chemostat. Here, we study a model of the chemostat involving the ﬂocculating and
• Mathematics
AIMS Mathematics
• 2021
This paper investigates a chemostat model with wall growth and Haldane consumption kinetics. In addition, bounded random fluctuations on the input flow, which are modeled by means of the well-known
• Mathematics
Mathematical Modelling and Control
• 2021
In this paper we study some chemostat models with random bounded fluctuations on the input flow. We start with the classical chemostat system and obtain new models incorporating, for instance, wall
• Environmental Science
SIAM J. Appl. Math.
• 2000
A mathematical model of microbial competition for limiting nutrient and wall-attachment sites in a chemostat, formulated by Freter et al, is mathematically analyzed and two bistable scenarios are of more relevance to the colonization resistance phenomena.
• Engineering
SIAM J. Appl. Math.
• 2000
A surprising finding in the case of two-strain competition is the existence of a steady state solution characterized by the segregation of the two bacterial strains to separate nonoverlapping segments along the tubular reactor.
• Mathematics
• 2008
In this paper, we introduce and study a model of a Beddington–DeAngelis type food chain chemostat with periodically varying substrate. We investigate the subsystem with substrate and prey and study
• Biology
• 2015
The newly developing theory ofnonautonomous dynamical systems provides the necessary concepts, in particular that of a nonautonomous pullback attractor, to analyze the dynamical behavior of nonaut autonomous chemostat models with or without wall growth, time-dependent delays, variable inputs and outputs.

## References

SHOWING 1-10 OF 20 REFERENCES

• Mathematics
• 1992
A model of exploitative competition of n species in a chemostat for a single, essential, nonreproducing, growth-limiting resource is considered. S. B. Hsu [SIAM J. Appl. Math., 34 (1978), pp.
• Biology
Biotechnology and bioengineering
• 1983
The present article considers the case where the attached cells form no more than a monolayer, and finds that in most of the possible cases, the two competitors can coexist in a stable steady state for a wide range of the operating parameters space.
• Physics
• 1995
THE THEORY OF THE CHEMOSTAT DYNAMICS OF MICROBIAL COMPETITION In this site isn`t the same as a solution manual you buy in a book store or download off the web. Our Over 40000 manuals and Ebooks is
Discrete dynamical systems: Limit sets Stability of invariant sets and asymptotically smooth maps Examples of asymptotically smooth maps Dissipativeness and global attractors Dependence on parameters
Two competition models concerning n species consuming a single, limited resource are discussed. One is based on the Holling-type functional response and the other on the Lotka–Volterra-type. The
At its 1993 annual meeting, the American Society for Microbiology deemed the biofilm mode of growth to be a concept worthy of an extraordinary 4-day colloquium consisting of 52 lectures from invited
Conditions are presented under which the solutions of asymptotically autonomous differential equations have the same asymptotic behavior as the solutions of the associated limit equations. An example
Monotone dynamical systems Stability and convergence Competitive and cooperative differential equations Irreducible cooperative systems Cooperative systems of delay differential equations Quasimonotone systems of parabolic equations A competition model Appendix Bibliography.