Effect of anti-predator behaviour in a prey-predator system with strong Allee effect in prey population

Abstract

In this work a predator-prey model is proposed where prey species shows anti-predator behaviour to save themselves from predator's attack. Moreover, a strong Allee effect has been introduced in the prey population to make the model more realistic to the environment. Both generalist and specialist predators have been taken to observe the system dynamics minutely. Stability analysis has been performed for all the equilibrium points which shows that the trivial equilibrium point is a saddle for generalist predator but stable for the specialist predator. Routh-Hurwitz criterion gives the conditions for the local stability of the equilibrium points and the results give that the system does not exhibit any oscillating behaviour in presence of generalist predator. Numerical simulation supports the analytical findings. The predator population decreases with increasing value of `coefficient of rate of anti-predator behaviour' when generalist predator is considered but in presence of the specialist predator, the predator population first increases up to a threshold value and then decreases. It means a very small rate of anti-predation does not affect the predator's growth very much but if prey attacks the predator at a larger rate, then the predator population decreases. Also, the existence of one dimensional and two-dimensional bifurcations have been observed by making different parameters as bifurcating parameters around the critical points.