Interplay between fear in prey and mutual interference among predators in ecological systems: stability and bifurcation analysis

Due to fear of predation, prey populations adopt various anti-predator defense strategies,which reduce their birth rate. Here, we formulate both autonomous and non-autonomousprey-predator systems with the assumptions that the preys per capita birth rate decreasesas a consequence of fear of predators, and that predator species waste time searching forprey species due to encounters with other predators. For the autonomous system, we establishthe criteria under which the system is uniformly persistent and those under which thecoexistence equilibrium point is globally asymptotically stable. Moreover, the existence oflocal bifurcations, one- and two-parameter bifurcation analyses, and the influence of eachecological parameter on system dynamics are rigorously examined. For the non-autonomoussystem, we establish the conditions for uniform persistence and prove the existence of aunique globally asymptotically stable periodic solution under certain conditions.