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International Journal of Differential Equations
Volume 2011 (2011), Article ID 259805, 28 pages
http://dx.doi.org/10.1155/2011/259805
Research Article

Existence and Global Attractivity of Positive Periodic Solutions for a Two-Species Competitive System with Stage Structure and Impulse

1Guizhou Key Laboratory of Economics System Simulation, School of Mathematics and Statistics, Guizhou College of Finance and Economics, Guiyang 550004, China
2Faculty of Science, Hunan Institute of Engineering, Xiangtan 411004, China

Received 10 August 2011; Accepted 17 September 2011

Academic Editor: Yuji Liu

Copyright © 2011 Changjin Xu and Daxue Chen. 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 class of nonautonomous two-species competitive system with stage structure and impulse is considered. By using the continuation theorem of coincidence degree theory, we derive a set of easily verifiable sufficient conditions that guarantee the existence of at least a positive periodic solution, and, by constructing a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are presented. Finally, an illustrative example is given to demonstrate the correctness of the obtained results.