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Hopf bifurcation and global stability for a delayed predator-prey system with stage structure for predator. (English) Zbl 1151.34067
Summary: A delayed predator-prey system with stage structure for the predator is 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 the time delay $\tau ^{*}$ is sufficiently small, while loss of stability by a Hopf bifurcation can occur as the delay increases.

##### MSC:
 34K60 Qualitative investigation and simulation of models 34K18 Bifurcation theory of functional differential equations 34K20 Stability theory of functional-differential equations 92D25 Population dynamics (general) 34K13 Periodic solutions of functional differential equations
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##### References:
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