Copyright © 2010 Qiuying Li et al. 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 discrete predator-prey system with time delay and feedback controls is studied. Sufficient conditions which guarantee the predator and the prey to be permanent are obtained. Moreover, under some suitable conditions, we show that the predator species y will be driven to extinction. The results indicate that one can choose suitable controls to make the species coexistence in a long term.