Bifurcations and vertical distribution in a nonlocal phytoplankton-nutrient-detritus model

Abstract

This study investigates a nonlocal reaction-diffusion-advection model for phytoplankton-nutrient-detritus systems, focusing on the existence of positive steady states and their vertical distribution. A significant challenge arises from the nonlocal reaction term, which invalidates the standard comparison principle. We address this issue by introducing weighted cumulative distribution functions to establish the global boundedness of the solutions. Additionally, we tackle the non-monotonicity introduced by detritus recycling through scaling transformations. Our findings reveal a complex bifurcation structure: lower phytoplankton mortality rates enhance their persistence, while the presence of detritus enables the existence of multiple steady states. Spatially, we observe that phytoplankton concentrations tend to aggregate at the surface or the bottom of the water column when advection dominates diffusion. In contrast, under strong diffusion, phytoplankton distributions become uniform, while nutrient distributions remain heterogeneous. These results provide insights into the nonlinear mechanisms that govern spatial heterogeneity in aquatic ecosystems.