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The Scientific World Journal
Volume 2013 (2013), Article ID 137384, 9 pages
http://dx.doi.org/10.1155/2013/137384
Research Article

A Mathematical Model with Pulse Effect for Three Populations of the Giant Panda and Two Kinds of Bamboo

1College of Forestry, Beijing Forestry University, Beijing 100083, China
2College of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan, 464000, China
3School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, China

Received 2 October 2013; Accepted 31 October 2013

Academic Editors: J. Banas, F. J. Garcia-Pacheco, and S. A. Mohiuddine

Copyright © 2013 Xiang-yun Shi and Guo-hua Song. 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 mathematical model for the relationship between the populations of giant pandas and two kinds of bamboo is established. We use the impulsive perturbations to take into account the effect of a sudden collapse of bamboo as a food source. We show that this system is uniformly bounded. Using the Floquet theory and comparison techniques of impulsive equations, we find conditions for the local and global stabilities of the giant panda-free periodic solution. Moreover, we obtain sufficient conditions for the system to be permanent. The results provide a theoretical basis for giant panda habitat protection.