Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional Response

We study the qualitative behavior of a class of predator-prey models with Beddington-DeAngelis-type functional response, primarily from the viewpoint of permanence (uniform persistence). The Beddington-DeAngelis functional response is similar to the Holling type-II functional response but contains a...

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Bibliographic Details
Published in:Differential equations & nonlinear mechanics 2010, Vol.2010 (2010), p.1-24
Main Authors: Khellaf, Wahiba, Hamri, Nasreddine
Format: Article
Language:English
Subjects:
Colleges & universities
Criteria
Differential equations
Growth rate
Interference
Lyapunov functions
Mathematical models
Nonlinearity
Per capita
Predators
Stability
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Summary:We study the qualitative behavior of a class of predator-prey models with Beddington-DeAngelis-type functional response, primarily from the viewpoint of permanence (uniform persistence). The Beddington-DeAngelis functional response is similar to the Holling type-II functional response but contains a term describing mutual interference by predators. We establish criteria under which we have boundedness of solutions, existence of an attracting set, and global stability of the coexisting interior equilibrium via Lyapunov function.
ISSN:1687-9643
1687-4099
1687-9651
1687-4102
DOI:10.1155/2010/813289