منابع مشابه
Coexistence of Competing Predators in a Chemostat
An analysis is given of a mathematical model of two predators feeding on a single prey growing in the chemostat. In the case that one of the predators goes extinct, a global stability result is obtained. Under appropriate circumstances, a bifurcation theorem can be used to show that coexistence of the predators occurs in the form of a limit cycle.
متن کاملCrowding effects promote coexistence in the chemostat∗
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...
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 کاملCoexistence phenomena and global bifurcation structure in a chemostat-like model with species-dependent diffusion rates.
We study the competition of two species for a single resource in a chemostat. In the simplest space-homogeneous situation, it is known that only one species survives, namely the best competitor. In order to exhibit coexistence phenomena, where the two competitors are able to survive, we consider a space dependent situation: we assume that the two species and the resource follow a diffusion proc...
متن کاملFeedback-mediated Coexistence and Oscillations in the Chemostat
We consider a mathematical model that describes the competition of three species for a single nutrient in a chemostat in which the dilution rate is assumed to be controllable by means of state dependent feedback. We consider feedback schedules that are affine functions of the species concentrations. In case of two species, we show that the system may undergo a Hopf bifurcation and oscillatory b...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1990
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181073042