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Discrete Dynamics in Nature and Society
Volume 2016, Article ID 2560195, 9 pages
http://dx.doi.org/10.1155/2016/2560195
Research Article

Dynamics of a Seasonally Forced Phytoplankton-Zooplankton Model with Impulsive Biological Control

Department of Mathematics, Sichuan Minzu College, Kangding 626001, China

Received 27 May 2016; Accepted 22 June 2016

Academic Editor: Darko Mitrovic

Copyright © 2016 Jianglin Zhao and Yong Yan. 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 paper investigates the dynamics of a seasonally forced phytoplankton-zooplankton model with impulsive biological control. It shows that the periodic eradicated solution is unstable. Further, the condition for permanence of the system is established by relations between the model parameters and the intensity of the impulses. The numerical analysis is performed to study the effect of seasonality and impulsive perturbations on plankton dynamics. The numerical results imply that the seasonal forcing can trigger more periodic mode and the impulsive period for control of the size of phytoplankton is more practicable to the system than the impulsive release of zooplankton. These conclusions provide a better understanding of controlling harmful algae blooms.