International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 64, Pages 4057-4070

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

Copyright © 2003 Qiming Liu and Rui Xu. 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.


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.