Journal of Applied Mathematics
Volume 2013 (2013), Article ID 101238, 9 pages
Research Article

An Impulsive Periodic Single-Species Logistic System with Diffusion

Chenxue Yang,1,2 Mao Ye,1,2 and Zijian Liu3,4

1School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
2State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210093, China
3School of Science, Chongqing Jiaotong University, Chongqing 400074, China
4Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China

Received 11 January 2013; Accepted 17 April 2013

Academic Editor: Michael Meylan

Copyright © 2013 Chenxue Yang et al. 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.


We study a single-species periodic logistic type dispersal system in a patchy environment with impulses. On the basis of inequality estimation technique, sufficient conditions of integrable form for the permanence and extinction of the system are obtained. By constructing an appropriate Lyapunov function, conditions for the existence of a unique globally attractively positive periodic solution are also established. Numerical examples are shown to verify the validity of our results and to further discuss the model.