Global Dynamics of a Toxin Producing Phytoplankton–Zooplankton System in an Advective Environment

In this paper, we mainly focus on global dynamics of a toxin producing phytoplankton–zooplankton system in an advective environment. We first investigate the well‐posedness of solution. Then, we investigate properties of semitrivial steady state. And by studying the influence of the diffusive rates and on , we obtain stability of the semitrivial steady state. We also prove the existence and uniqueness of positive steady state by bifurcation theory. We numerically analyze how the rate of toxin liberation by phytoplankton and the advection rate caused by unidirectional water flow affect the persistence and spatial distribution of the phytoplankton and zooplankton. Numerical simulations validate our theoretical results.