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On the dynamics of predator-prey models with the Beddington-DeAngelis functional response. (English) Zbl 0991.34046
The dynamics of predator-prey models with Holling-type II functional response is well known. So is the main dynamics of pure ratio-dependent predator-prey models with Holling-type II functional response. It is now known that these models pale in comparison to Beddington-DeAngelis-type predator-prey models when confronted with real data. Although the Beddington-DeAngelis-type predator-prey model has been around for over two decades, there has been little qualitative work done on it.
This paper provides a first attempt on the mathematical analysis of this model and its direct extension to a spatially heterogeneous setting (a reaction-diffusion model). The main results are criteria for permanence and for predator extinction. Recently, it is known (Tzy-Wei Hwang, personal communication (2002)) that the positive steady state of the ODE Beddington-DeAngelis-type predator-prey model is globally stable if it is locally stable.
Reviewer: Kuang Yang (Tempe)

MSC:
34D23 Global stability of solutions to ordinary differential equations
92D25 Population dynamics (general)
34D05 Asymptotic properties of solutions to ordinary differential equations
35K57 Reaction-diffusion equations
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