Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China
Copyright © 2011 Yakui Xue and Xiafeng Duan. 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.
We invest a predator-prey model of Holling type-IV functional response with stage structure and double delays due to maturation time
for both prey and predator. The dynamical behavior of the system is investigated from the point of view of stability switches aspects. We assume that the
immature and mature individuals of each species are divided by a fixed age,
and the mature predator only attacks the mature prey. Based on some comparison arguments, sharp threshold conditions which are both necessary and
sufficient for the global stability of the equilibrium point of predator extinction
are obtained. The most important outcome of this paper is that the variation of
predator stage structure can affect the existence of the interior equilibrium point
and drive the predator into extinction by changing the maturation (through-stage) time delay. Our linear stability work and numerical results show that
if the resource is dynamic, as in nature, there is a window in maturation time
delay parameters that generate sustainable oscillatory dynamics.