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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 602679, 14 pages
http://dx.doi.org/10.1155/2012/602679
Research Article

Existence of at Least Two Periodic Solutions for a Competition System of Plankton Allelopathy on Time Scales

Department of Mathematics, Kunming University of Science and Technology, Yunnan 650093, China

Received 3 October 2011; Accepted 15 February 2012

Academic Editor: Meng Fan

Copyright © 2012 Hui Fang. 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 study a competition system of the growth of two species of plankton with competitive and allelopathic effects on each other on time scales. With the help of Mawhin’s continuation theorem of coincidence degree theory, a set of easily verifiable criteria is obtained for the existence of at least two periodic solutions for this model. Some new existence results are obtained. An example and numerical simulation are given to illustrate the validity of our results.