A nutrient-induced seasonal algal bloom model

A model for nutrient-phytoplankton dynamics is constructed and analyzed. We contribute theoretical analyses for a constant nutrient input and a time-varying nutrient input in terms of steady state, local and global stabilities, and limit cycle behavior. Numerical simulations of the model are carried out to examine the dynamics of the model for four types of nutrient input: 1) constant input, 2) sinusoidal input, 3) periodic step function input with fixed upper and lower amplitudes, 4) periodic step function input with time-varying upper and lower amplitudes. The numerical solutions confirm the non-oscillatory and oscillatory behaviors predicted from the theoretical analysis. It is shown that periodic nutrient inputs of types 2) and 3) cause phytoplankton blooms with periodic behavior and that changes in the frequency of the input produce blooms with a wide range of different dynamical behavior. It is found that nutrient inputs of type 4) give the best agreement between the model and the observed data.