International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 971427, 10 pages
http://dx.doi.org/10.1155/2012/971427
Research Article

On the Uniqueness and Dependence of Positive Periodic Solutions for Delay Differential Systems with Feedback Control

Haitao Li1 and Yansheng Liu2

1School of Control Science and Engineering, Shandong University, Jinan 250061, China
2Department of Mathematics, Shandong Normal University, Jinan 250014, China

Received 22 March 2012; Accepted 14 July 2012

Academic Editor: S. M. Gusein-Zade

Copyright © 2012 Haitao Li and Yansheng 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 paper investigates a class of delay differential systems with feedback control. Sufficient conditions are obtained for the existence and uniqueness of the positive periodic solution by utilizing some results from the mixed monotone operator theory. Meanwhile, the dependence of the positive periodic solution on the parameter 𝜆 is also studied. Finally, an example together with numerical simulations is worked out to illustrate the main results.