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Abstract and Applied Analysis
Volume 2014, Article ID 568943, 8 pages
http://dx.doi.org/10.1155/2014/568943
Research Article

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

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 24 February 2014; Accepted 13 March 2014; Published 8 April 2014

Academic Editor: Yonghui Xia

Copyright © 2014 Chaoqun Xu and Sanling Yuan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.