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Recently, by studying some field experimental data and research articles it has been observed that due to predation, predators not only affect prey by direct killing, but they also induce the predation fear in prey which reduces its reproduction rate. The grouping behaviour of animals is one of the most important and interesting phenomena in the field of population dynamics. As a result of prey-predator forming groups, many authors have considered different functional responses in their proposed models. In reality, the amount of biomass converted into the predator due to the prey consumption is not instantaneous. To incorporate the gestation delay in this paper we have proposed and analysed a delayed prey-predator model with square root functional response and fear effect in the prey. We have discussed the qualitative analysis of solutions of the considered model in presence and absence of delay. Moreover, the transcritical bifurcation, Hopf bifurcation with it’s direction and the impact of the fear effect on both populations are studied here. Finally, some numerical simulations through graphical illustrations are carried out to support the analytical results.. i

Complex dynamical behaviour of a delayed prey-predator model with square root functional response in presence of fear in the prey