Global dynamics of zooplankton and harmful algae in flowing habitats

This paper is devoted to the study of two advection–dispersion–reaction models arising from the dynamics of harmful algae and zooplankton in flowing-water habitats where a main channel is coupled to a hydraulic storage zone, representing an ensemble of fringing coves on the shoreline. For the system modeling the dynamics of algae and their toxin that contains little limiting nutrient, we establish a threshold type result on the global attractivity in terms of the basic reproduction ratio for algae. For the model with zooplankton that eat the algae and are inhibited by the toxin produced by algae, we show that there exists a coexistence steady state and the zooplankton is uniformly persistent provided that two basic reproduction ratios for algae and zooplankton are greater than unity.