Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 186539, 19 pages
Dynamics Behaviors of a Discrete Ratio-Dependent Predator-Prey System with
Holling Type III Functional Response and Feedback Controls
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 will be driven to extinction. Examples together with their numerical
simulations show that the main results are verifiable.