Abstract and Applied Analysis
Volume 2010 (2010), Article ID 845606, 24 pages
doi:10.1155/2010/845606
Research Article

Permanence and Extinction of a Generalized Gause-Type Predator-Prey System with Periodic Coefficients

Jinhuo Luo1,2

1School of Mathematical Sciences, Fudan University, Shanghai 200433, China
2College of Information Technology, Shanghai Ocean University, Shanghai 201306, China

Received 9 August 2010; Revised 8 December 2010; Accepted 17 December 2010

Academic Editor: Elena Litsyn

Copyright © 2010 Jinhuo Luo. 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

We study the permanence and extinction of a generalized Gause-type predator-prey system with periodic coefficients. We provide a sufficient and necessary condition to guarantee the predator and prey species to be permanent and a sufficient condition for the existence of a periodic solution. In addition we prove that when the predator population tends to extinction, the prey population keeps oscillating above a positive population level.