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Abstract and Applied Analysis
Volume 2014, Article ID 471507, 10 pages
Research Article

Stability and Hopf Bifurcation Analysis of a Nutrient-Phytoplankton Model with Delay Effect

1School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, China
2Zhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang 325035, China
3School of Life and Environmental Science, Wenzhou University, Wenzhou, Zhejiang 325035, China

Received 13 November 2013; Accepted 25 January 2014; Published 12 March 2014

Academic Editor: Imran Naeem

Copyright © 2014 Xinhong Pan et al. 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.


A delay differential system is investigated based on a previously proposed nutrient-phytoplankton model. The time delay is regarded as a bifurcation parameter. Our aim is to determine how the time delay affects the system. First, we study the existence and local stability of two equilibria using the characteristic equation and identify the condition where a Hopf bifurcation can occur. Second, the formulae that determine the direction of the Hopf bifurcation and the stability of periodic solutions are obtained using the normal form and the center manifold theory. Furthermore, our main results are illustrated using numerical simulations.