Abstract
A mathematical model connecting epilimnion and hypolimnion is proposed to describe the competition of phytoplankton for nutrients and light in a stratified lake. The existence and stability of nonnegative steady-state solutions are completely characterized for all possible parameter ranges by means of stability analysis, bifurcation theory, and extensive simulations. The critical thresholds for settling speed of phytoplankton cells in the thermocline and the loss rate of phytoplankton are established, which determine the survival or extirpation of phytoplankton in epilimnion and hypolimnion. In particular, it is shown that in two extreme cases, the principle of competitive exclusion always holds in a stratified lake. We also consider the influence of environmental parameters on the vertical distribution and biomass density of phytoplankton via a systematic sensitivity analysis, and investigate their roles in phytoplankton blooms. These results can be used for the prediction of phytoplankton competition and blooms in a stratified lake.
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