Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 186539, 19 pages
doi:10.1155/2008/186539

Dynamics behaviors of a discrete ratio-dependent predator-prey system with Holling type III functional response and feedback controls

Abstract

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.