Dynamic Analysis of a Predator–Prey System in Advective Environments With Weak Allee Effects: The Effects of Boundary Conditions

ABSTRACT This paper investigates the dynamics of a predator–prey model with weak Allee effect on prey under different boundary conditions in advective environments. Through theoretical analysis, we fully characterize the system's dynamical behaviors in the parameter space including the Allee threshold, advection rate, mortality rate of predator. In open environments (NF/FF or NF/H), the system exhibits three distinct states: extinction of both species, survival of only prey, and coexistence of both species. We find that a lower weak Allee threshold promotes the possibility of extinction for both species. In closed environments (NF/NF), the system admits no extinction state, and independent of the Allee effect, the semi‐trivial steady state always exists.