Impact of fear in a prey-predator system with herd behaviour

Abstract Fear of predation plays an important role in the growth of a prey species in a prey-predator system. In this work, a two-species model is formulated where the prey species move in a herd to protect themselves and so it acts as a defense strategy. The birth rate of the prey here is affected due to fear of being attacked by predators and so, is considered as a decreasing function. Moreover, there is another fear term in the death rate of the prey population to emphasize the fact that the prey may die out of fear of predator too. But, in this model, the function characterizing the fear effect in the death of prey is assumed in such a way that it is increased only up to a certain level. The results show that the system performs oscillating behavior when the fear coefficient implemented in the birth of prey is considered in a small amount but it changes its dynamics through Hopf bifurcation and becomes stable for a higher value of the coefficient. Regulating the fear terms ultimately makes an impact on the growth of the predator population as the predator is taken as a specialist predator here. The increasing value of the fear terms (either implemented in birth or death of prey) decrease the count of the predator population with time. Also, the fear implemented in the birth rate of prey makes a higher impact on the growth of the predator population than in the case of the fear-induced death rate.