International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 891812, 18 pages
doi:10.1155/2010/891812

Analysis of a nonautonomous delayed predator-prey system with a stage structure for the predator in a polluted environment

Abstract

A two-species nonautonomous Lotka-Volterra type model with diffusional migration among the immature predator population, constant delay among the matured predators, and toxicant effect on the immature predators in a nonprotective patch is proposed. The scale of the protective zone among the immature predator population can be regulated through diffusive coefficients Di(t), i=1,2. It is proved that this system is uniformly persistent (permanence) under appropriate conditions. Sufficient conditions are derived to confirm that if this system admits a positive periodic solution, then it is globally asymptotically stable.