A Phytoplankton Bloom Model with Seasonal Nutrient Input

A model for nutrient-phytoplankton dynamics is constructed and analyzed. A theoretical analysis shows that changes in the nutrient input can significantly change the qualitative behavior of the phytoplankton dynamics. In particular, the behavior can change from asymptotically stable to periodic. Numerical solutions of the model are carried out for seasonal nutrient inputs of a range of different frequencies and amplitudes. The numerical solutions confirm the non-oscillatory and oscillatory behaviors predicted from the theoretical analysis. The numerical simulations show that a periodic nutrient input can cause phytoplankton blooms and that changes in the frequency of the input can produce blooms with a wide range of different dynamical behaviors. In addition, it is shown that in some regions of parameter space, the oscillatory behavior recurs annually and agrees with observational data. Key-Words: Bloom dynamics, Frequencies, Nutrient-phytoplankton interaction, Oscillatory behavior, Periodically forced damped system, Seasonal nutrient input.