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

Analysis of a Nonautonomous Delayed Predator-Prey System with a Stage Structure for the Predator in a Polluted Environment

G. P. Samanta1,2

1Mathematical Institute, Slovak Academy of Sciences, Stefanikova 49, 81473 Bratislava, Slovakia
2Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah-711103, India

Received 3 July 2009; Accepted 7 February 2010

Academic Editor: Harvinder S. Sidhu

Copyright © 2010 G. P. Samanta. 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

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.