The existence, bifurcation and stability of positive stationary solutions of a diffusive Leslie–Gower predator–prey model with Holling-type II functional responses

In this paper, we revisit a diffusive Leslie–Gower predator–prey model with Holling-type II functional responses and Dirichlet boundary condition. It is shown that multiple positive steady state solutions exist under certain conditions on the parameters, while for another parameter region, the positive steady state solution is unique and locally asymptotically stable. Results are proved by using bifurcation theory, fixed point index theory, energy estimates and asymptotic behavior analysis.