Abstract and Applied Analysis

Stability and Hopf Bifurcation in a Delayed Predator-Prey System with Herd Behavior

Chaoqun Xu and Sanling Yuan

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Abstract

A special predator-prey system is investigated in which the prey population exhibits herd behavior in order to provide a self-defense against predators, while the predator is intermediate and its population shows individualistic behavior. Considering the fact that there always exists a time delay in the conversion of the biomass of prey to that of predator in this system, we obtain a delayed predator-prey model with square root functional response and quadratic mortality. For this model, we mainly investigate the stability of positive equilibrium and the existence of Hopf bifurcation by choosing the time delay as a bifurcation parameter.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 568943, 8 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425048254

Digital Object Identifier
doi:10.1155/2014/568943

Mathematical Reviews number (MathSciNet)
MR3198213

Zentralblatt MATH identifier
07022627

Citation

Xu, Chaoqun; Yuan, Sanling. Stability and Hopf Bifurcation in a Delayed Predator-Prey System with Herd Behavior. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 568943, 8 pages. doi:10.1155/2014/568943. https://projecteuclid.org/euclid.aaa/1425048254


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