A diffusive predator-prey system with prey refuge and predator cannibalism

This paper is devoted to exploring a diffusive predator-prey system with prey refuge and predator cannibalism. We investigate dynamics of this system, including dissipation and persistence, local and global stability of constant steady states, Turing instability, and nonexistence and existence of nonconstant steady state solutions. The influence of prey refuge and predator cannibalism on predator and prey biomass density is also considered by using a systematic sensitivity analysis. Our studies suggest that appropriate predator cannibalism has a positive effect on predator biomass density, and then high predator cannibalism may stabilize the predator-prey ecosystem and prevent the paradox of enrichment.