Differential Equations and Nonlinear Mechanics

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

Wahiba Khellaf and Nasreddine Hamri

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Abstract

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.

Article information

Source
Differ. Equ. Nonlinear Mech., Volume 2010 (2010), Article ID 813289, 24 pages.

Dates
Received: 17 September 2009
Accepted: 19 April 2010
First available in Project Euclid: 26 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1485399708

Digital Object Identifier
doi:10.1155/2010/813289

Mathematical Reviews number (MathSciNet)
MR2683913

Zentralblatt MATH identifier
1204.34066

Citation

Khellaf, Wahiba; Hamri, Nasreddine. Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional Response. Differ. Equ. Nonlinear Mech. 2010 (2010), Article ID 813289, 24 pages. doi:10.1155/2010/813289. https://projecteuclid.org/euclid.ijde/1485399708


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