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Volume 11,     Number 1,     Spring 2003

 

ANALYSIS OF A CLASS OF MONOD-LIKE FUNCTIONS THAT LINK SPECIFIC GROWTH RATE TO DELAYED GROWTH RESPONSE
SEAN ELLERMEYER

Abstract. We analyze a family of functions that provide a link between specific growth rate (x'(t) / x(t)) and delayed growth response (DGR) in a class of delay differential equation models for microbial growth in batch and continuous culture. The connection between specific growth rate and delayed growth response, which has not been considered in previous studies of these models, is then employed in studying a model of continuous culture competition between two species of microorganisms that are "Monod-equivalent" in that they have the same maximal specific growth rate (µm) and half- saturation constant (Kh). It is shown that the species with the smaller DGR is a superior competitor if the dilution rate of the chemostat is high but that the species with the larger DGR is a better competitor if the dilution rate is low.

 

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