Dynamics of a diffusive predator–prey model with modified Leslie–Gower schemes and additive Allee effect

Abstract

In this paper, we consider a diffusive predator–prey model with modified Leslie–Gower schemes and additive Allee effect on prey under homogeneous Neumann boundary condition. Firstly, we investigate the qualitative properties of the system including the persistent property, and local and global asymptotical stability of the unique positive constant equilibrium point of the system. Next, we also show the existence and nonexistence of nonconstant positive steady states of the reaction–diffusion system, which reflect the effect of large diffusivity.