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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 823026, 8 pages
Research Article

Dynamical Analysis of a Nitrogen-Phosphorus-Phytoplankton Model

Yunli Deng,1,2 Min Zhao,2,3 Hengguo Yu,1,2 and Yi Wang1,2

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 Sciences, Wenzhou University, Wenzhou, Zhejiang 325027, China

Received 7 October 2014; Accepted 23 November 2014

Academic Editor: Garyfalos Papashinopoulos

Copyright © 2015 Yunli Deng 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.


This paper presents a nitrogen-phosphorus-phytoplankton model in a water ecosystem. The main aim of this research is to analyze the global system dynamics and to study the existence and stability of equilibria. It is shown that the phytoplankton-eradication equilibrium is globally asymptotically stable if the input nitrogen concentration is less than a certain threshold. However, the coexistence equilibrium is globally asymptotically stable as long as it exists. The system is uniformly persistent within threshold values of certain key parameters. Finally, to verify the results, numerical simulations are provided.