Asymmetric diffusion of prey in predation systems with multiple patches

This paper considers predator-prey systems with multiple patches, where individuals of the prey move among patches. Rigorous analysis on the model shows nonnegativeness and boundedness of the solutions. Further study shows conditions by which the system admits an equilibrium that is globally asymptotically stable. For two-patch systems, it is shown that varying the diffusion of prey could make the predator transition between persisting in two patches, survival only in one of the patches, and extinction in both patches in a smooth fashion. For multi-patch systems, it is shown that the diffusion of prey could lead to a win-win situation, where total population abundances of both prey and predator are larger than those without dispersal, which extends previous theory. A novel prediction of this work is that the preference in diffusion could lead to the increase of population abundance, even lead to the maximal abundance. These results are important in ecological conservation and management.