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

H. L. Smith; X. Q. Zhao

doi:10.3934/dcdsb.2001.1.183

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2001, Volume 1, Issue 2: 183-191. Doi: 10.3934/dcdsb.2001.1.183

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

H. L. Smith^1, and
X. Q. Zhao^2,

1.
Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804
2.
Department of Mathematics and Statistics, Memorial University of Newfoundland, St John's, NF A1C 5S7

Revised: January 2001

Published: May 2001

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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 first author [11] where the case $m = 2$ was treated.

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Mathematics Subject Classification: 34C35, 92A15.

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