Journal of Applied Mathematics
Volume 2004 (2004), Issue 3, Pages 255-270
doi:10.1155/S1110757X04308090

Periodic solutions of a delayed predator-prey model with stage structure for predator

Rui Xu,1,2 M. A. J. Chaplain,2 and F. A. Davidson2

1Department of Mathematics, Institute of Shijiazhuang Mechanical Engineering, Hebei Province, Shijiazhuang 050003, China
2Department of Mathematics, University of Dundee, Dundee DD1 4HN, UK

Received 28 August 2003; Revised 2 February 2004

Copyright © 2004 Rui Xu et al. 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 periodic time-dependent Lotka-Volterra-type predator-prey model with stage structure for the predator and time delays due to negative feedback and gestation is investigated. Sufficient conditions are derived, respectively, for the existence and global stability of positive periodic solutions to the proposed model.