Relaxation oscillations and other non-Michaelian behavior in a slow-fast phytoplankton growth model | Relaxation oscillations and other non-Michaelian behavior in a slow-fast phytoplankton growth model [Physiological model of nutrient uptake, biomass growth, batch cultures and lakes]
1984
A physiological model of nutrient uptake, based on an enzyme mechanism for membrane transport, is combined with a phytoplankton biomass growth equation based on internal nutrient limitation. The system of equations thus obtained can model phytoplankton growth with a considerably richer dynamics than the Michaelis-Menten-Monod (M3) model or the Droop model. In particular, since the characteristic time scale of nutrient uptake is considerably faster than that of biomass increase, a singular perturbation problem results, leading to relaxation oscillations (similar to the Van der Pol oscillator) and other non-Michaelian type long-term dynamical behavior. In contrast with both the Michaelis-Menten-Monod model and the Droop model, which were developed using steady-state chemostat data, the present model would seem to be appropriate for batch cultures and lakes with long turnover times, where the assumptions of the chemostat steady state are not fulfilled. Three sets of data are cited which circumstantially support the model suggesting that the hypothesized uptake mechanism may warrant further experimental investigation.
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