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.
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 |
Keywords:
predator-prey models; Beddington-DeAngelis functional response; permanence; predator extinctionReferences:
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