Article

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

Discrete and Continuous Dynamical Systems-series B - DISCRETE CONTIN DYN SYS-SER B 05/2000; 1(2). DOI: 10.3934/dcdsb.2001.1.183

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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.01/2014: pages 1-19; - [Show abstract] [Hide abstract]

**ABSTRACT:**We present a size-structured model which describes the dynamics of n ecotypes competing for common resources. We prove that if reproduction is closed, i.e., offspring of one ecotype belongs to the same ecotype, then competitive exclusion between these ecotypes will occur. We give conditions on the model parameters which determine the fittest ecotype that wins the competition. Furthermore, we show that if reproduction is open then coexistence between the n ecotypes is possible.Natural Resource Modeling 06/2008; 17(3):213 - 228. · 0.49 Impact Factor -
##### Article: N-species non-autonomous Lotka–Volterra competitive systems with delays and impulsive perturbations

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**ABSTRACT:**In this paper, a class of non-autonomous N-species Lotka–Volterra-type competitive system with time delays and impulsive perturbations is investigated. New criteria on coexistence and global attractivity for all species other than some inclining to extinction are established. From our results, we find that the extinction of some species due to competition exclusion and weak adaption to a stochastically variable environment characterized by impulsive perturbations is necessary for the coexistence and global attractivity of other survivors in a limited resource ecosystem. Meanwhile, the dynamic behaviors of competition models with impulse perturbations are more complicated and different from prior research results obtained from continuous competition models. The impulse perturbations impose either negative or positive influences on the survival of species, which results in evidently regulative effects, and even make the inferior competitors exclude or coexist with the superior competitors. The theoretical results are confirmed by a special example and numerical simulations, by which we find some interesting phenomena.Nonlinear Analysis Real World Applications 05/2011; · 2.20 Impact Factor

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