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

Permanence of a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay

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.