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论文类型：期刊论文

发表时间：2011-04-15

发表刊物：APPLIED MATHEMATICS AND COMPUTATION

收录刊物：Scopus、SCIE、EI

卷号：217

期号：16

页面范围：6934-6949

ISSN号：0096-3003

关键字：Chemostat; Competition; Reaction-diffusion system; Fixed point index; Attractor; Coexistence; Persistence; Extinction

摘要：This paper studies a un-stirred chemostat with two species competing for two growth-limiting, non-reproducing resources. We determine the conditions for positive steady states of the two species, and then consider the global attractors of the model. In addition, we obtain the conditions under which the two populations uniformly strongly persist or go to extinction. Since the diffusion mechanism with homogeneous boundary conditions inhibits the growth of the organism species, it can be understood that the coexistence will be ensured by proportionally smaller diffusions for the two species. In particular, it is found that both instability and bi-stability subcases of the two semitrivial steady states are included in the coexistence region. The two populations will go to extinction when both possess large diffusion rates. If just one of them spreads faster with the other one diffusing slower, then the related semitrivial steady state will be globally attracting. The techniques used for the above results consist of the degree theory, the semigroup theory, and the maximum principle. (C) 2011 Elsevier Inc. All rights reserved.