On the Dynamics of Predator–Prey Models with the Beddington–DeAngelis Functional Response

The dynamics of predator–prey models with the Beddington–DeAngelis functional response are analyzed, primarily from the viewpoint of permanence (uniform persistence). The Beddington–DeAngelis functional response is similar to the Holling type 2 functional response but contains an extra term describing mutual interference by predators. Both spatially homogeneous models based on ordinary differential equations and reaction–diffusion models are considered. Criteria for permanence and for predator extinction are derived. For systems without diffusion or with no-flux boundary conditions, criteria are derived for the existence of a globally stable coexistence equilibrium or, alternatively, for the existence of periodic orbits.