Global boundedness and dynamics of a diffusive predator–prey model with modified Leslie–Gower functional response and density-dependent motion

Abstract

This paper is devoted to studying the dynamical behaviors and stationary patterns of a diffusive modified Leslie–Gower predator–prey model with density-dependent motion in the predator population. We establish the existence of classical solutions with the uniform-in time bound and then analyze the local and global stability of the spatially homogeneous co-existence steady state under certain parametric conditions. By choosing the prey diffusion rate d2 as the bifurcation parameter, the steady state bifurcations from the positive constant equilibrium solution are investigated. Numerical simulations are performed to corroborate our analytical findings.