Competition in the Chemostat: Some Remarks
نویسندگان
چکیده
1 Review of competition for a single substrate Paul Waltman’s chemostat-related work has had a large impact in population biology, ecology and bio-engineering. It has motivated and inspired the work of many other authors, including us. It seems appropriate to point out a major open problem which remains unresolved after more than thirty years and to touch on some other issues related to bacterial ecology in the chemostat. The basic equations for mixed culture competition in the chemostat for a single growth-limiting substrate are given by [8, 26, 29]:
منابع مشابه
A Model of the Effect of Anti-competitor Toxins on Plasmid-bearing, Plasmid-free Competition
The usual models of the chemostat assume that the competition is purely exploitative, the competition is only through the consumption of the nutrient. However, it is known that microorganisms can produce toxins against its competitors. In this work, we consider a model of competition in the chemostat between plasmid-bearing, plasmid-free organisms for a single nutrient where plasmid-bearing org...
متن کاملA numerical method for discrete fractional--order chemostat model derived from nonstandard numerical scheme
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 ...
متن کاملGlobal Stability for a Model of Competition in the Chemostat with Microbial Inputs
We propose a model of competition of n species in a chemostat, with constant input of some species. We mainly emphasize the case that can lead to coexistence in the chemostat in a non-trivial way, i.e., where the n − 1 less competitive species are in the input. We prove that if the inputs satisfy a constraint, the coexistence between the species is obtained in the form of a globally asymptotica...
متن کاملA Mathematical Model of Competition for Two Essential Resources in the Unstirred Chemostat
A mathematical model of competition between two species for two growth-limiting, essential (complementary) resources in the unstirred chemostat is considered. The existence of a positive steady-state solution and some of its properties are established analytically. Techniques include the maximum principle, the fixed point index, and numerical simulations. The simulations also seem to indicate t...
متن کاملCompetition and coexistence in the chemostat∗
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...
متن کامل