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

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 d 2 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. • We establish the existence of classical solutions for a diffusive modified Leslie–Gower predator prey model. • We analyze the local and global stability of the spatially homogeneous co-existence steady state. • The steady state bifurcations from the positive constant equilibrium solution are investigated. [ABSTRACT FROM AUTHOR]