# American Institute of Mathematical Sciences

May  2001, 1(2): 183-191. doi: 10.3934/dcdsb.2001.1.183

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

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

Revised  January 2001 Published  February 2001

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.
Citation: H. L. Smith, X. Q. Zhao. Competitive exclusion in a discrete-time, size-structured chemostat model. Discrete & Continuous Dynamical Systems - B, 2001, 1 (2) : 183-191. doi: 10.3934/dcdsb.2001.1.183
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