A Discrete-delayed Model with Plasmid-bearing, Plasmid-free Competition in a Chemostat
نویسندگان
چکیده
A discrete-delayed model of plasmid-bearing, plasmid-free organisms competing for a single-limited nutrient in a chemostat is established. Rigorous mathematical analysis of the asymptotic behavior of this model is presented. An interesting method to analyze the local stability of interior equilibrium is developed. The argument is also applicable to a model of plasmidbearing, plasmid-free organisms competing for two complementary nutrients in a chemostat.
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 کاملCompetition between Plasmid-Bearing and Plasmid-Free Organisms in a Chemostat with Pulsed Input and Washout
We consider a model of competition between plasmid-bearing and plasmid-free organisms in the chemostat with pulsed input and washout. We investigate the subsystem with nutrient and plasmid-free organism and study the stability of the boundary periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields the invasion ...
متن کاملPeriodic solutions in a model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor.
We obtain necessary and sufficient conditions on the existence of a unique positive equilibrium point and a set of sufficient conditions on the existence of periodic solutions for a 3-dimensional system which arises from a model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor. Our results improve the corresponding results obtained by Hsu, Luo, ...
متن کاملGlobal analysis of a model of plasmid-bearing, plasmid-free competition in a chemostat
A model of competit ion between plasmid-bearing and plasmid-free organisms in a chemostat was proposed in a paper of Stephanopoulis and Lapidus. The model was in the form of a system of nonlinear ordinary differential equations. Such models are relevant to commercial production by genetically altered organisms in continuous culture. The analysis there was local (using index arguments). This pap...
متن کاملCompetition between Plasmid-bearing and Plasmid-free Microorganisms in a Chemostat with Distinct Removal Rates
In this paper we consider a competition model between plasmid-bearing and plasmid-free organisms in a chemostat that incorporates both general response functions and distinct removal rates. The model with identical removal rates was proposed in a paper of Stephanopoulis and Lapidus, and the analysis there was local. The complete global analysis of the model in the case of identical removal rate...
متن کامل