Competitive exclusion in a discrete-time, size-structured chemostat model

Discrete and Continuous Dynamical Systems - Series B (Impact Factor: 0.63). 05/2000; 1(2). DOI: 10.3934/dcdsb.2001.1.183

ABSTRACT Competitive exclusion is proved for a discrete-time, size-structured, nonlinear matrix model of m-species competition in the chemostat. The winner is the population able to grow at the lowest nutrient concentration. This extends the results of earlier work of the rst author 11] where the case m = 2 was treated.

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    ABSTRACT: Age is an important factor in the dynamics of epidemic processes. Great attention has been paid to continuous age-structured epidemic models. The discrete epidemic models are in their infancy. In this paper, a discrete age-structured epidemic SIS model is formulated. The dynamical behavior of this model is studied. The basic reproductive number is defined and a threshold for the persistence or extinction of disease is found.
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    ABSTRACT: In biology, the principle of competitive exclusion, largely attributed to the Russian biologist G. F. Gause, states that two species competing for common resources (food, territory etc.) cannot coexist, and that one of the species drives the other to extinction. We make a survey of discrete-time mathematical models that address this issue and point out the main mathematical methods used to prove the occurrence of competitive exclusion in these models. We also offer examples of models in which competitive exclusion fails to take place, or at least it is not the only outcome. Finally, we present an extension of the competitive exclusion results in [1, 5] to a more general model.
    THEORY AND APPLICATIONS OF DIFFERENCE EQUATIONS AND DISCRETE DYNAMICAL SYSTEMS; Springer Proceedings in Mathematics & Statistics 102, Edited by Z. Alsharawi, J.M. Cushing, S. Elaydi, 01/2014: chapter Competitive Exclusion Through Discrete Time Models: pages 1-19; Springer-Verlag Berlin Heidelberg.


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