For a stage-structured population model in periodic discrete habitat, with periodic initial values it reduces to a system of two differential equations with time delay. Assuming the birth rate is of unimodal type, we obtain the influence of time delay on the local and global dynamics. In particular, large delay leads to population vanishing. As delay decreases, we found three critical values of delay for the emergence of different dynamics, by appealing to a combination of monotone dynamical system theory, Hopf bifurcation theory and the fluctuation method. Numerical simulations are also performed to illustrate the results.

中文翻译：

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在离散周期生境中的阶段结构种群模型：III。单峰增长和延迟效应

对于具有周期性初始值的周期性离散栖息地的阶段结构种群模型，其简化为具有时滞的两个微分方程组。假设出生率是单峰型，我们得到时延对局部和全局动力学的影响。特别是，大的延误导致人口消失。随着延迟的减小，我们通过结合单调动力学系统理论，Hopf分叉理论和涨落方法的组合，发现了三个因不同动力学而出现的延迟临界值。还进行了数值模拟以说明结果。