Effects of Fear and Additional Food in a Delayed Predator–Prey Model

Abstract

A field observation on a terrestrial vertebrate has shown that the fear of predators can affect the behavior of prey populations and it can greatly reduce their reproduction. On the other hand, it has been observed that providing additional food to the predator decreases the predatory attack rate and increases the growth rate of the predator. In this paper, we have investigated the dynamical behavior of a predator–prey model incorporating both the effects of fear and additional food. Positivity, uniform boundedness and extinction criteria of the system are studied. Equilibrium points and their stability behaviors are also discussed here. Existence of a Hopf-bifurcation is established by considering the level of fear as bifurcation parameter. The effect of time-delay is discussed, where the delay may be considered as gestation time of the predator. Numerical simulations are performed using MATLAB to verify our analytical findings.