A coupled plankton system with instantaneous and delayed predation.

We present two simple plankton population models: one has instantaneous predation, another has delayed predation. The models consist of two coupled differential equations representing the interaction between phytoplankton and herbivorous zooplankton with additional effect of zooplankton predation by a constant fish population. We study the dynamical behaviour and investigate the conditions to guarantee the coexistence of two species, and address the stability and bifurcation under different density of fish, with or without the maturation time delay. Analytical methods and numerical simulations are used to obtain information about the qualitative behaviour of the models.