中文摘要：

针对具有年龄结构和扩散的林蛙时滞增长模型，以时滞为分支参数，研究了系统的线性稳定性，获得了系统存在Hopf分支的充分条件，分析了林蛙年龄结构、扩散率和时滞对该系统动力学的影响．

英文摘要：

A delayed rana growth model with stage structure and dispersion was investigated. By choosing the delay as a bifurcation parameter, we studied the linear stability of the system, and obtained the existence sufficient conditions of Hopf bifurcation for the system, and analyzed the dynamical influences caused by the stage structure of rana and dispersion and de- layed.