Original Article
Kyungpook Mathematical Journal 2004; 44(4): 519-535
Published online December 23, 2004
Copyright © Kyungpook Mathematical Journal.
Periodic Solutions of a Delayed Population Model with One Predator and Two Preys
Rui Xu1 , M. A. J. Chaplain2 , F. A. Davidson2
1Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, Hebei Province, P. R. China
2Department of Mathematics, University of Dundee, Dundee DD1 4HN, UK
A delayed periodic Lotka-Volterra predator-prey model with one predator and two preys is investigated. By using Gaines and Mawhin’s continuation theorem of coincidence degree theory and by constructing appropriate Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions to the model.
Keywords: predator-prey model, time delay, periodic solution, global stability