Dynamics of a Diffusive Predator–Prey System with Fear Effect in Advective Environments

We explore a diffusive predator–prey system that incorporates the fear effect in advective environments. First, we analyze the eigenvalue problem and the adjoint operator, considering Constant-Flux and Dirichlet boundary conditions, as well as Free-Flow boundary conditions. Next, we use the principle of comparison to prove the non-negativity of the solution. Our investigation focuses on determining the direction and stability of spatial Hopf bifurcation, with the generation delay serving as the bifurcation parameter. Additionally, we examine the influence of both linear and Holling-II functional responses on the dynamics of the model. Through these analyses, we gain better understanding of the intricate relationship among advection, predation, and prey response in this system.