Qualitative analysis of a Hölling-Tanner predator-prey model with mutual interference

A reaction-diffusion system arising from the Hölling-Tanner predator-prey model is proposed and mutual interference among predators is considered. Conditions for the local and global asymptotical stability of equilibrium solutions are given by means of analyzing eigenvalue spectrum as well as Lyapunov functionals. Some non-existence results of non-constant positive steady-state solutions are obtained. Also, the numerical simulation is given to verify the theoretical results.