On the dynamics of predator-prey models with the Beddington-DeAngelis functional response

The dynamics of predator-prey models with the Beddington-DeAngelis function al response are analyzed, primarily from the viewpoint of permanence (unifo rm persistence). The Beddington-DeAngelis functional response is similar to the Holling type 2 functional response but contains an extra term describi ng mutual interference by predators. Both spatially homogeneous models base d on ordinary differential equations and reaction-diffusion models are cons idered. Criteria for permanence and fur predator extinction are derived. Fo r systems without diffusion or with no-flux boundary conditions, criteria a re derived for the existence of a globally stable coexistence equilibrium o r, alternatively, for the existence of periodic orbits. (C) 2001 Academic P ress.