Population dynamics and competition in chemostat models with adaptive nutrient uptake |
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Authors: | Betty Tang Ann Sitomer Trachette Jackson |
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Institution: | (1) Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, USA, US |
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Abstract: | The standard Monod model for microbial population dynamics in the chemostat is modified to take into consideration that cells
can adapt to the change of nutrient concentration in the chemostat by switching between fast and slow nutrient uptake and
growing modes with asymmetric thresholds for transition from one mode to another. This is a generalization of a modified Monod
model which considers adaptation by transition between active growing and quiescent cells. Global analysis of the model equations
is obtained using the theory of asymptotically autonomous systems. Transient oscillatory population density and hysteresis
growth pattern observed experimentally, which do not occur for the standard Monod model, can be explained by such adaptive
mechanism of the cells. Competition between two species that can switch between fast and slow nutrient uptake and growing
modes is also considered. It is shown that generically there is no coexistence steady state, and only one steady state, corresponding
to the survival of at most one species in the chemostat, is a local attractor. Numerical simulations reproduce the qualitative
feature of some experimental data which show that the population density of the winning species approaches a positive steady
state via transient oscillations while that of the losing species approaches the zero steady state monotonically.
Received 4 August 1995; received in revised form 15 December 1995 |
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Keywords: | : Monod model Chemostat Competition Adaptive nutrient uptake |
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