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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 741043, 11 pages
http://dx.doi.org/10.1155/2013/741043
Research Article

Existence and Stability of Positive Periodic Solutions for a Neutral Multispecies Logarithmic Population Model with Feedback Control and Impulse

1Department of Mathematics, National University of Defense Technology, Changsha 410073, China
2Department of Mathematics, Hengyang Normal University, Hengyang, Hunan 421008, China

Received 14 June 2013; Revised 1 August 2013; Accepted 2 August 2013

Academic Editor: Yong Ren

Copyright © 2013 Zhenguo Luo and Liping Luo. 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 investigate a neutral multispecies logarithmic population model with feedback control and impulse. By applying the contraction mapping principle and some inequality techniques, a set of easily applicable criteria for the existence, uniqueness, and global attractivity of positive periodic solution are established. The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases. We also give an example to illustrate the applicability of our results.