Impact of Diffusion and Advection on Phytoplankton–Zooplankton Dynamics in River Ecosystems

This paper examines a reaction–diffusion–advection system modeling the interactions between phytoplankton and zooplankton in river ecosystems. Due to spatial heterogeneity and complex boundary conditions, the principal eigenvalue of the system does not exhibit monotonicity with respect to diffusion and advection coefficients, making it challenging to analyze its dynamics. To address this, we developed various nonmonotonic parameter analysis techniques to study the stability of the semi-trivial steady state under varying zooplankton diffusion and advection rates in both open and closed environments. Using global bifurcation theory and parabolic equation dynamics, we identify three dynamic regimes: extinction, coexistence, and persistence of phytoplankton. Coexistence occurs in closed environments with low zooplankton mortality, while in open environments, a small advection rate is necessary. For moderate zooplankton mortality, specific combinations of advection and diffusion parameters also support coexistence. Numerical simulations confirm the significant influence of diffusion, advection, and mortality on system dynamics. These results highlight key ecological factors that drive plankton population stability and coexistence in aquatic ecosystems.