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2014 Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and Delays
Nai-Wei Liu, Ting-Ting Kong
Abstr. Appl. Anal. 2014(SI13): 1-8 (2014). DOI: 10.1155/2014/930762


We consider a predator-prey system with Beddington-DeAngelis functional response and delays, in which not only the stage structure on prey but also the delay due to digestion is considered. First, we give a sufficient and necessary condition for the existence of a unique positive equilibrium by analyzing the corresponding locations of a hyperbolic curve and a line. Then, by constructing an appropriate Lyapunov function, we prove that the positive equilibrium is locally asymptotically stable under a sufficient condition. Finally, by using comparison theorem and the ω -limit set theory, we study the global asymptotic stability of the boundary equilibrium and the positive equilibrium, respectively. Also, we obtain a sufficient condition to assure the global asymptotic stability.


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Nai-Wei Liu. Ting-Ting Kong. "Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and Delays." Abstr. Appl. Anal. 2014 (SI13) 1 - 8, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07023333
MathSciNet: MR3216082
Digital Object Identifier: 10.1155/2014/930762

Rights: Copyright © 2014 Hindawi


Vol.2014 • No. SI13 • 2014
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