Impact of Fear Cost and Time Lag on the Dynamics of an Ecological System of Two Competing Predators and One Prey

The aim of this paper is to discover the impact of the fear of predators in prey and time lag corresponding to the gestation period on the dynamics of a food web model including two competing predator species and one prey species. Existence, non-negativity and boundedness of the model solutions are examined. An attractive region for the model is found. The permanence of the model, under certain conditions is proved. The criteria for the existence of all biologically feasible equilibrium points of the proposed model are determined. Locally asymptotically stability as well as globally stability of the model equilibrium points without time lag has been explored. Locally dynamics and the Hopf bifurcation near planar equilibrium points of the model with existence of time lag are studied. It is determined critical value for time lag, where the model under goes Hopf -bifurcation near planar equilibrium points. Finally, with the help of MATLAB program, the model solved numerically, it was discovered that, the dynamics of the model may induce a transition from the stability situation to the state where the populations oscillate periodically, when the value of fear level decreases. But when the value of time lag increases, the dynamics of the system may induce a transition from the a stability situation to the state where the populations oscillate periodically.