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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 815682, 11 pages
http://dx.doi.org/10.1155/2015/815682
Research Article

Spatiotemporal Complexity of the Nutrient-Phytoplankton 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 25 September 2014; Revised 3 January 2015; Accepted 13 January 2015

Academic Editor: Giovanni Garcea

Copyright © 2015 Debing Mei 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 consider the mathematical formulation, analysis, and numerical solution of a nonlinear system of nutrient-phytoplankton, which consists of a series of reaction-advection-diffusion equations. We derive the critical conditions for Turing instability without an advection term and define the range of Turing instability with the change of nutrient concentration. We show that horizontal movement of phytoplankton could influence the system and that it is unstable when the horizontal velocity exceeds a critical value. We also compare reaction-diffusion equations with reaction-advection-diffusion equations through simulations, with spotted, banded, and crenulate patterns produced from our model. We found that different spatial constructions could occur, impacted by the diffusion and sinking of nutrients and phytoplankton. The new model may help us better understand the dynamics of an aquatic community.