Dynamical analysis on a predator-prey model with stage structure and mutual interference

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.