GLOBAL STABILITY AND HOPF BIFURCATION OF A DELAYED PREDATOR-PREY MODEL INCORPORATING ALLEE EFFECT AND FEAR EFFECT

This paper aims to discover the impact of the fear of predators in prey, Allee effect for predator reproduction and time delay corresponding to the gestation period on the dynamics of a predator- prey model. Existence, non-negativity, and boundedness of the model solutions are guaranteed. The criteria for asymptotically stability of all the biologically feasible steady state points are determined. It is also determined a critical value for time delay, where the model under goes Hopf -bifurcation near coexistence steady state point. Finally, with the help of the MATLAB program, to confirm the analytical results and discover the impact of fear, the Allee effect, and time delay, the model was solved numerically.it is observed that fear affect negatively on both prey and predator species and the time delay may system may induce a transition of the dynamics of system from the a stability situation to the state where the populations oscillate periodically or vice versa