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Mathematical Problems in Engineering
Volume 2014, Article ID 586262, 8 pages
http://dx.doi.org/10.1155/2014/586262
Research Article

Chaotic Dynamic Analysis of Aquatic Phytoplankton System

1Graduate Institute of Precision Manufacturing, National Chin-Yi University of Technology, Taichung 41170, Taiwan
2Department of Industrial Education and Technology, National Changhua University of Education, Changhua 500, Taiwan

Received 3 May 2014; Accepted 25 May 2014; Published 25 June 2014

Academic Editor: Her-Terng Yau

Copyright © 2014 C. C. Wang and C. C. Liu. 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

This study analyzed the effect of nonlinear dynamic parameter of phytoplankton toxin emission on the system. Many previous studies have indicated that the zooplankton, mollusks, and habitat factors generate nonlinear chaotic dynamic behavior, which is hardly controlled random behavior. Therefore, in order to understand in what parameter conditions the system has this nonlinear behavior, the linear and nonlinear behaviors resulting from different conditions are discussed. This study used numerical analysis of differential transformation method to analyze the phase of system and applied bifurcation diagrams, trajectory diagrams, Poincaré maps, and spectrograms to discuss and validate whether the system has chaos phenomenon.