THE EFFECT OF REFUGE AND PROPORTIONAL HARVESTING FOR A PREDATOR-PREY SYSTEM WITH REACTION-DIFFUSION

A diffusive predator-prey system with Holling-Tanner functional response and no-flux boundary condition is considered in this work. By using upper and lower solutions combined with iteration method, sufficient condition which ensures the global asymptotical stability of the unique positive equilibrium of the system is obtained. It is shown that the prey refuge and the proportional harvesting can influence the global asymptotical stability of unique positive equilibrium of the system, furthermore, they can change the position of the unique interior equilibrium and make species coexist more easily.