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 fur 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. (C) 2001 Academic Press.