Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 202, Issue 2, Pages 721-729Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2008.03.011
Keywords
global asymptotic stability; Hopf bifurcation; stage structure; predator-prey; time delay; permanence
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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.
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