Journal of Applied Mathematics
Volume 2013 (2013), Article ID 679602, 17 pages
http://dx.doi.org/10.1155/2013/679602
Research Article

On the Nature of Bifurcation in a Ratio-Dependent Predator-Prey Model with Delays

Changjin Xu1 and Yusen Wu2

1Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550004, China
2Department of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China

Received 1 April 2013; Revised 29 May 2013; Accepted 2 June 2013

Academic Editor: Jinde Cao

Copyright © 2013 Changjin Xu and Yusen Wu. 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 ratio-dependent predator-prey model with two delays is investigated. The conditions which ensure the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are obtained. It shows that the two different time delays have different effects on the dynamical behavior of the system. An example together with its numerical simulations shows the feasibility of the main results. Finally, main conclusions are included.