In this paper, we formulate a stage-structured predator–prey model with mutual interference, in which includes two discrete delays. By theoretical analysis, we establish the stability of the unique positive equilibrium and the existence of Hopf bifurcation when the maturation delay for predators is used as the bifurcation parameter. Our results exhibit that the maturation delay for preys does not affect the stability of the positive equilibrium. However, the maturation delay for predator is able to destabilize the positive equilibrium and causes periodic solutions. Numerical simulations are carried out to illustrate the theoretical results and display the differential impacts of two type delays and mutual interference.

在本文中，我们建立了具有相互干扰的阶段结构的捕食者－被捕食者模型，其中包括两个离散的延迟。通过理论分析，建立了以捕食者的成熟延迟为分岔参数的唯一正平衡的稳定性和Hopf分岔的存在。我们的结果表明，猎物的成熟延迟不影响正平衡的稳定性。但是，捕食者的成熟延迟会破坏正平衡的稳定性并引起周期解。进行了数值模拟，以说明理论结果并显示两种类型的延迟和相互干扰的不同影响。