Modeling Predator–Prey Systems with Strong Allee Effect and Mutual Interference among Predators

In this paper, we develop two prey–predator systems: a prey–specialist predator system and a prey–generalist predator system. The Crowley–Martin functional response is used to model the time wasted by a predator in handling captured prey and in encounters with other predators. The prey–specialist predator system undergoes codimension-1 bifurcations, such as transcritical, saddle-node, and Hopf bifurcations, as well as codimension-2 bifurcations, including cusp, Bogdanov–Takens, and Bautin bifurcations. There exists a threshold value of the handling time, above which the predator species cannot survive. For handling time below this threshold, either both species survive or become extinct together, depending on the time wasted due to predator interference and the initial densities of the species. However, no such threshold exists for the handling time in the prey–generalist predator system. This system undergoes a saddle-node bifurcation. Higher values of mutual interference enhance the coexistence of both species in the environment. However, their coexistence again depends on their initial densities. An interesting feature of both systems is that the equilibrium prey density increases while the equilibrium predator density decreases as the time wasted due to encounters with other predators increases.