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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 451757, 10 pages
http://dx.doi.org/10.1155/2014/451757
Research Article

Nonlinear Dynamics of a Nutrient-Plankton Model

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 11 October 2013; Revised 3 December 2013; Accepted 4 December 2013; Published 16 January 2014

Academic Editor: Malay Banerjee

Copyright © 2014 Yapei Wang 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.

Abstract

We investigated a nonlinear model of the interaction between nutrients and plankton, which was addressed using a pair of reaction-advection-diffusion equations. Based on numerical analysis, we studied a model without diffusion and sinking terms, and we found that the phytoplankton density (a stable state) increased with the increase of nutrient density. We analyzed the model using a linear analysis technique and found that the sinking of phytoplankton could affect the system. If the sinking velocity exceeded a certain critical value, the stable state became unstable and the wavelength of phytoplankton increased with the increase of sinking velocity. Furthermore, band patterns were also produced by our model, which was affected by the diffusion and sinking of phytoplankton. Thus, the change in the diffusion and sinking of phytoplankton led to different spatial distributions of phytoplankton. All of these results are expected to be useful in the study of plankton dynamics in aquatic ecosystems.