A MODIFIED LESLIE-GOWER FRACTIONAL ORDER PREY-PREDATOR INTERACTION MODEL INCORPORATING THE EFFECT OF FEAR ON PREY

In this article, a Leslie-Gower type predator prey model with fear effect has been proposed and studied in the framework of fractional calculus in Caputo sense. The well-posedness of the system has been verified analytically. The states of stability of the possible non-negative equilibrium points have been derived. It is observed that both the fear level and memory bound of the interacting species take crucial part in determining the states of stability of the system dynamics around the co-existence equilibrium point. The fear level makes the system stable around the positive equilibrium point via two consecutive Hopf bifurcations. The higher memory of the interacting species leads to stabilization of the ecological model system whether fading memory has destabilization role in the system dynamics. The analytical representations of the bifurcation scenarios have been rigorously analyzed. Also, it has been observed that the corresponding integer order model system may experience saddle-node bifurcation depending upon the change of suitable parameter. All our observations have been captured in numerical simulation portion and detailed explanations of the outcomes of the numerical simulation have been represented.