Original Article
Kyungpook Mathematical Journal 2010; 50(2): 255-266
Published online June 23, 2010
Copyright © Kyungpook Mathematical Journal.
Global Periodic Solutions in a Delayed Predator-Prey System
with Holling II Functional Response
Zhichao Jiang, Hongtao Wang, Hongmei Wang
Fundamental Science Department, North China Institute of Astronautic Engineer- ing, Hebei, Langfang, 065000, China,
Heibei College of Finance, Hebei, Baoding, 071051, China,
North China Electric Power University, Hebei, Baoding, 071051, China
Received: June 23, 2010; Revised: June 23, 2010; Accepted: June 23, 2010
We consider a delayed predator-prey system with Holling II functional response.
Firstly, the paper considers the stability and local Hopf bifurcation for a delayed
prey-predator model using the basic theorem on zeros of general transcendental function,
which was established by Cook etc.. Secondly, special attention is paid to the global existence
of periodic solutions bifurcating from Hopf bifurcations. By using a global Hopf
bifurcation result due to Wu , we show that the local Hopf bifurcation implies the global
Hopf bifurcation after the second critical value of delay. Finally, several numerical simulations
supporting the theoretical analysis are given.
Keywords: Time delay, Hopf bifurcation, Numerical simulations