Dynamical behavior of a delayed diffusive predator–prey model with competition and type III functional response

In this paper, a delayed diffusive predator–prey model with competition and type III functional response is investigated. By using inequality analytical technique, some sufficient conditions which ensure the permanence of the model have been derived. By Lyapunov functional method, a series of sufficient conditions which assure the global asymptotic stability of the system are established. The paper ends with some numerical simulations that illustrate our analytical predictions.