Abstract and Applied Analysis
Volume 2009 (2009), Article ID 960823, 6 pages
doi:10.1155/2009/960823
Research Article

Permanence of a Semi-Ratio-Dependent Predator-Prey System with Nonmonotonic Functional Response and Time Delay

Xuepeng Li and Wensheng Yang

School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian 350007, China

Received 14 May 2009; Accepted 28 July 2009

Academic Editor: Paul Eloe

Copyright © 2009 Xuepeng Li and Wensheng 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.

Abstract

Sufficient conditions for permanence of a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay x˙1(t)=x1(t)[r1(t)−a11(t)x1(t−τ(t))−a12(t)x2(t)/(m2+x12(t))],  x˙2(t)=x2(t)[r2(t)−a21(t)x2(t)/x1(t)], are obtained, where x1(t) and x2(t) stand for the density of the prey and the predator, respectively, and m≠0 is a constant. τ(t)≥0 stands for the time delays due to negative feedback of the prey population.