Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 186539, 19 pages
Research Article

Dynamics Behaviors of a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls

Jinghui Yang

College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, China

Received 24 April 2008; Revised 16 August 2008; Accepted 2 October 2008

Academic Editor: Juan Jose Nieto

Copyright © 2008 Jinghui Yang. 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.


A ratio-dependent predator-prey system with Holling type III functional response and feedback controls is proposed. By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the system are obtained. After that, under some suitable conditions, we show that the predator species y will be driven to extinction. Examples together with their numerical simulations show that the main results are verifiable.