Fear-driven extinction and (de)stabilization in a predator-prey model incorporating prey herd behavior and mutual interference

<abstract><p>The indirect effect of predation due to fear has proven have adverse effects on the reproductive rate prey population. Here, we present a deterministic two-species predator-prey model with herd behavior, mutual interference, and fear. We give conditions for existence some local global bifurcations at coexistence equilibrium. also show that can induce extinction population from zone in finite time. Our numerical simulations reveal varying strength predators suitable choice parameters stabilize destabilize equilibrium solutions model. Further, discuss outcome introducing constant harvesting effort predator terms changing dynamics system, particular, time stable coexistence.</p></abstract>