Global Behavior for a Strongly Coupled Predator-Prey Model with One Resource and Two Consumers. (7th August 2012)

• Record Type: Journal Article
• Authors: Jiao, Yujuan; Fu, Shengmao
• Other Names: Bertsch Michiel Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-08-07
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/183285
• Languages: English
• ISSNs: 1085-3375

Abstract

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.