  A deterministic two-species predator-prey model with prey herd behavior is
considered incorporating mutual interference and the effect of fear. We provide
guidelines to the dynamical analysis of biologically feasible equilibrium
points. We give conditions for the existence of some local and global
bifurcations at the coexistence equilibrium. We also show that fear can induce
extinction of the prey population from a coexistence zone in finite time. Our
numerical simulations reveal that varying the strength of fear of predators
with suitable choice of parameters can stabilize and destabilize the
coexistence equilibrium solutions of the model. Additionally, we discuss the
outcome of introducing a constant harvesting effort to the predator population
in terms of changing the dynamics of the system, in particular, from finite
time extinction to stable coexistence. Furthermore, we perform extensive
numerical experiments to visualize the dynamical behavior of the model and
substantiate the results we obtained.
