Permanence and periodic solution for a modified Leslie-Gower type predator-prey model with diffusion and non constant coefficients

In this paper we study a predator-prey system, modeling the interaction of two species with diffusion and T-periodic environmental parameters. It is a Leslie-Gower type predator-prey model with Holling-type-II functional response. We establish some sufficient conditions for the ultimate boundedness of solutions and permanence of this system. By constructing an appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Numerical simulations are presented to illustrate the results