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Discrete Dynamics in Nature and Society
Volume 2011, Article ID 163541, 17 pages
http://dx.doi.org/10.1155/2011/163541
Research Article

Complex Behavior in a Fish Algae Consumption Model with Impulsive Control Strategy

1School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, China
2School of Life and Environmental Science, Wenzhou University, Wenzhou, Zhejiang 325035, China

Received 9 August 2011; Accepted 27 August 2011

Academic Editor: M. De la Sen

Copyright © 2011 Jin Yang and Min Zhao. 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 a dynamic mathematical model of fish algae consumption with an impulsive control strategy analytically. It is proved that the system has a globally asymptotically stable algae-eradication periodic solution and is permanent by using the theory of impulsive equations and small-amplitude perturbation techniques. Numerical results for impulsive perturbations demonstrate the rich dynamic behavior of the system. Further, we have also compared biological control with chemical control. All these results may be useful in controlling eutrophication.