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In this paper, we investigate the global dynamics of a Leslie-Gower predator-prey system in advective homogeneous environments. We discuss the existence and uniqueness of positive steady-state solutions. We study the large time behavior of solutions and establish threshold conditions for persistence and extinction of two species when they live in open advective environments. Numerical simulations indicate that the introduction of advection leads to the evolution of spatial distribution patterns of species and specially it may induce spatial separation of the prey and predator under some conditions.

Threshold dynamics of a reaction-diffusion-advection Leslie-Gower predator-prey system