A Hölling's type II prey-predator model with stage structure and nonlocal delay

In this paper, a prey-predator model with reaction-diffusion is investigated under homogenous Neumann boundary condition. By taking food ingestion and species' moving into account, model is further coupled with Hölling's type II function response and nonlocal delay. Sufficient conditions for the global stability of three equilibria, i.e. positive, semi-trivial and trivial steady states are mainly derived by Lyapunov functional, respectively. Results show that intra-specific competition benefits the coexistence of prey and predator. Numerical simulations are performed to illustrate the analytical results.