Population abundance in predator-prey systems with predator's dispersal between two patches

This paper considers predator-prey systems in which the predator moves between two patches. One patch is a source, where the predator and prey can persist, while the other is a sink where the predator cannot survive. Our aim is to show whether or not the dispersal is beneficial to the predator's total abundance at equilibrium. Using dynamical systems theory, we demonstrate conditions under which a dispersing predator can persist. Our analysis shows that the predator equilibrium abundance at intermediate dispersal rates can be higher than that without dispersal, while extremely large or small dispersal rates could result in predator's extinction. Moreover, we find an explicit expression for the total abundance, which clearly shows the role of dispersal rates and asymmetry on the predator's abundance. Numerical simulations confirm and extend our results.