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

✍ Scribed by Robert Stephen Cantrell; Chris Cosner

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
129 KB
Volume
257
Category
Article
ISSN
0022-247X

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✦ Synopsis

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.

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