Pattern analysis of a modified Leslie–Gower predator–prey model with Crowley–Martin functional response and diffusion

In this paper, we study a modified Leslie–Gower predator–prey model with Crowley–Martin functional response and spatial diffusion under homogeneous Neumann boundary condition, and obtain some important qualitative properties, including the existence of the global positive solution, the dissipation and persistence of the two species, the local and global asymptotic stability of the constant equilibria, and Hopf bifurcation around the interior constant equilibrium. In addition, we establish the existence and nonexistence of nonconstant positive steady states.