Journal of Applied Mathematics
Volume 2012 (2012), Article ID 452789, 17 pages
http://dx.doi.org/10.1155/2012/452789
Research Article

A Mathematical Model for the Dynamics of a Fish Algae Consumption Model with Impulsive Control Strategy

Jin Yang1 and Min Zhao2

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

Received 21 October 2011; Accepted 7 February 2012

Academic Editor: Leevan Ling

Copyright © 2012 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

A dynamic mathematical model of fish algae consumption with an impulsive control strategy is proposed and analyzed in detail. It is shown that the system has a globally asymptotically stable algae-eradication periodic solution which can be obtained using the Floquet theory of impulsive differential equations and small-amplitude perturbation techniques. The conditions for the permanence of the system can also be determined. Numerical results for impulsive perturbations show the rich dynamic behavior of the system. All these results may be useful in controlling eutrophication.