Abstract and Applied Analysis

Global Behavior for a Strongly Coupled Predator-Prey Model with One Resource and Two Consumers

Yujuan Jiao and Shengmao Fu

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Abstract

We consider a strongly coupled predator-prey model with one resource and two consumers, in which the first consumer species feeds on the resource according to the Holling II functional response, while the second consumer species feeds on the resource following the Beddington-DeAngelis functional response, and they compete for the common resource. Using the energy estimates and Gagliardo-Nirenberg-type inequalities, the existence and uniform boundedness of global solutions for the model are proved. Meanwhile, the sufficient conditions for global asymptotic stability of the positive equilibrium for this model are given by constructing a Lyapunov function.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 183285, 25 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1355495806

Digital Object Identifier
doi:10.1155/2012/183285

Mathematical Reviews number (MathSciNet)
MR2959743

Zentralblatt MATH identifier
1246.35105

Citation

Jiao, Yujuan; Fu, Shengmao. Global Behavior for a Strongly Coupled Predator-Prey Model with One Resource and Two Consumers. Abstr. Appl. Anal. 2012 (2012), Article ID 183285, 25 pages. doi:10.1155/2012/183285. https://projecteuclid.org/euclid.aaa/1355495806


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