Qualitative analysis of Beddington–DeAngelis type impulsive predator–prey models

In the paper, the impulsive predator–prey models with Beddington–DeAngelis functional response are studied. Conditions for the existence and stability of a prey-free solution and for the existence of a nontrivial periodic solution have been established. Also, we find a sufficient condition that the model is permanent and show that the model has complex dynamical behaviors via bifurcation diagrams.