## Abstract and Applied Analysis

### Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and Delays

#### Abstract

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 $\omega$-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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 930762, 8 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412279726

Digital Object Identifier
doi:10.1155/2014/930762

Mathematical Reviews number (MathSciNet)
MR3216082

Zentralblatt MATH identifier
07023333

#### Citation

Liu, Nai-Wei; Kong, Ting-Ting. Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and Delays. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 930762, 8 pages. doi:10.1155/2014/930762. https://projecteuclid.org/euclid.aaa/1412279726

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