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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 495072, 13 pages
http://dx.doi.org/10.1155/2013/495072
Research Article

Hopf Bifurcation Analysis for a Semiratio-Dependent Predator-Prey System with Two Delays

Software College, Pingdingshan University, Pingdingshan 467000, China

Received 12 August 2013; Accepted 25 August 2013

Academic Editor: Massimiliano Ferrara

Copyright © 2013 Ming Zhao. 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

This paper is concerned with a semiratio-dependent predator-prey system with nonmonotonic functional response and two delays. It is shown that the positive equilibrium of the system is locally asymptotically stable when the time delay is small enough. Change of stability of the positive equilibrium will cause bifurcating periodic solutions as the time delay passes through a sequence of critical values. The properties of Hopf bifurcation such as direction and stability are determined by using the normal form method and center manifold theorem. Numerical simulations confirm our theoretical findings.