Dynamical analysis of predator–prey system with fear effect delay and maturation delay

This paper studies the dynamics of predator–prey system with stage structure for prey, where fear effect delay and maturation delay for prey coexist. First we study the existence of equilibrium points, the positivity, boundedness and permanence of solution of system, then we study the influence of two delays on the dynamics of system. We conclude that: (1) maturation delay can change the density of predator and prey, (2) Hopf bifurcation occurs as any of two delays increases and (3) delay of fear effect can lead to stability switch of system.