The periodically forced Droop model for phytoplankton growth in a chemostat |
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Authors: | H L Smith |
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Institution: | (1) Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, USA (halsmith@math.la.asu.edu, US |
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Abstract: | It is proved that the periodically forced Droop model for phytoplankton growth in a chemostat has precisely two dynamic regimes
depending on a threshold condition involving the dilution rate. If the dilution rate is such that the sub-threshold condition
holds, the phytoplankton population is washed out of the chemostat. If the super-threshold condition holds, then there is
a unique periodic solution, having the same period as the forcing, characterized by the presence of the phytoplankton population,
to which all solutions approach asymptotically. Furthermore, this result holds for a general class of models with monotone
growth rate and monotone uptake rate, the latter possibly depending on the cell quota.
Received 10 October 1995; received in revised form 26 March 1996 |
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Keywords: | : Chemostat Droop model Phytoplankton Global stability |
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