The periodically forced Droop model for phytoplankton growth in a chemostat

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.