中文摘要：

本文研究一类具有阶段结构的时滞Crowley—Martin功能反应型捕食者-食饵系统．通过分析特征根的分布情况得到正平衡点全局渐近稳定的充分条件与Hopf分支的存在性．利用规范型理论与中心流形定理，分析Hopf分支的方向和分支周期解的稳定性．最后数值模拟验证了分析结果的正确性．

英文摘要：

In this paper, we analyze a delayed and stage-structured predator-prey system with Crowley-Martin functional response. By analyzing the distribution of the roots of the associated characteristic equation, sufficient conditions for the local asymptotic stability of the positive equilibrium and the existence of the periodic solutions via Hopf bifurcation with respect to the time delay are obtained. Direction of the Hopf bifurcation and the stability of the periodic solutions that bifurcate from Hopf bifurcation are established by using the normal form theory and center manifold argument. Finally,numerical simulation results are given to support the analytical findings.