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Abstract and Applied Analysis
Volume 2013, Article ID 340174, 5 pages
http://dx.doi.org/10.1155/2013/340174
Research Article

Hopf-Pitchfork Bifurcation in a Phytoplankton-Zooplankton Model with Delays

School of Mathematics and Information Sciences, Henan University, Kaifeng 475001, China

Received 21 October 2013; Accepted 12 November 2013

Academic Editor: Allan Peterson

Copyright © 2013 Jia-Fang Zhang and Dan Zhang. 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

The purpose of this paper is to study the dynamics of a phytoplankton-zooplankton model with toxin delay. By studying the distribution of the eigenvalues of the associated characteristic equation, the pitchfork bifurcation curve of the system is obtained. Furthermore, on the pitchfork bifurcation curve, we find that the system can undergo a Hopf bifurcation at the positive equilibrium, and we derive the critical values where Hopf-Pitchfork bifurcation occurs.