International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 64, Pages 4057-4070
doi:10.1155/S0161171203211030

Periodic solution for a delayed three-species food-chain system with Holling type-II functional response

Qiming Liu1 and Rui Xu1,2

 1Department of Mathematics, Institute of Shijiazhuang Mechanical Engineering, Shijiazhuang 050003, China
2Department of Mathematics, University of Dundee, Dundee DD1 4HN, UK
Received 2 November 2002

Abstract

A delayed three-species periodic food-chain system with Holling type-II functional response is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, a set of easily verifiable sufficient conditions is derived for the existence of positive periodic solutions to the system.