A reaction-diffusion model of harmful algae and zooplankton in an ecosystem

This paper is devoted to the investigation of an unstirred chemostat system modeling the interactions of two essential nutrients (i.e., nitrogen and phosphorus), harmful algae (i.e., P. parvum and cyanobacteria), and a small-bodied zooplankton in an ecosystem. To obtain a weakly repelling property of a compact and invariant set on the boundary, we introduce an associated elliptic eigenvalue problem. It turns out that the model system admits a coexistence steady state and is uniformly persistent provided that the trivial steady state, two semi-trivial steady states and a global attractor on the boundary are all weak repellers.