Dynamics of a diffusive two-predator-one-prey model in advective heterogeneous environments

In this paper, we investigate the dynamics and asymptotic profiles of positive steady states of a general diffusive two-predator-one-prey model in advective heterogeneous environments. By the abstract persistence theory, the system is uniformly persistent under some assumptions, regardless of how the diffusion and advection rates vary. Furthermore, we analyze the role of advection on the limiting profiles of positive steady states. Our findings show that as the advection parameter varies, the limiting profile of positive steady states becomes very complicated, including multiple scenarios: coexistence (with multiple solutions) and extinction of the three species under different conditions. Finally, we demonstrate the correctness of the theoretical results and find some interesting phenomena through some numerical simulations.