Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 208167, 8 pages
Research Article

Global Asymptotic Stability of a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes

Sunshine College, Fuzhou University, Fuzhou, Fujian 350015, China

Received 3 April 2012; Accepted 22 May 2012

Academic Editor: Zhen Jin

Copyright © 2012 Shengbin Yu. 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 the predator-prey model proposed by Aziz-Alaoui and Okiye (Appl. Math. Lett. 16 (2003) 1069–1075) First, the structure of equilibria and their linearized stability is investigated. Then, we provide two sufficient conditions on the global asymptotic stability of a positive equilibrium by employing the Fluctuation Lemma and Lyapunov direct method, respectively. The obtained results not only improve but also supplement existing ones.