Global stability and bifurcation of time delayed prey-predator system incorporating prey refuge

► We describe a prey-predator model with Holling type II functional response incorporating prey refuge. ► The criterion for the existence of interior equilibrium point, stability and bifurcation of the system are derived. ► Density-dependent mortality rate for the predator is considered as bifurcation parameter to examine the occurrence of Hopf bifurcation phenomenon. ► Discrete-type gestational delay of predators is incorporated on the system and the dynamics of the delay induced prey-predator system is analyzed. ► Numerical simulations are carried out to verify the analytically proved results.