Hopf bifurcation and global stability for a delayed predator-prey system with stage structure for predator

In this paper, a delayed predator-prey system with stage structure for predator is proposed and studied. It is found that the time delay is harmless for permanence of the stage-structured system. If alpha beta < 1, sufficient conditions which guarantee the global stability of positive equilibrium are given. If alpha beta > 1, we show that the unique positive equilibrium is locally asymptotically stable when time delay tau* is sufficiently small, while loss of stability by a Hopf bifurcation can occur as the delay increases. (C) 2008 Elsevier Inc. All rights reserved.