International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 43, Pages 2307-2323

Sufficient and necessary condition for the permanence of periodic predator-prey system

Jingan Cui1 and Xinyu Song2

1Department of Mathematics, Nanjing Normal University, Nanjing 210097, China
2Department of Mathematics, Xinyang Teachers College, Henan, Xinyang 464000, China

Received 22 January 2003

Copyright © 2004 Jingan Cui and Xinyu Song. 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 consider the permanence of a periodic predator-prey system, where the prey disperse in a two-patch environment. We assume the Volterra within-patch dynamics and provide a sufficient and necessary condition to guarantee the predator and prey species to be permanent by using the techniques of inequality analysis. Our work improves previous relevant results.