A food chain model with Allee effect: Analysis on the behaviors of equilibria

The Allee effect is crucial to population ecology and conservation biology because it clarifies how difficult it can be for tiny populations to endure and expand. Low population densities make it more difficult for individuals to survive or reproduce in a phenomenon. Therefore, it is important to study the ecological system, including the Allee effect. Accordingly, our goal in this paper was to examine equilibria's behaviors in a three-species food chain model incorporating the Allee effect. This model includes a linear type of functional response. The points of equilibrium are categorized and depicted. The behaviors of these equilibrium points are then illustrated analytically through stability and bifurcation analyses. Moreover, the numerical simulation utilizes realistic hypothetical data to confirm the analytical results and detect the influence of varying the parameters on the system's dynamics. It is observed that the system undergoes bistable behavior; otherwise, the trivial equilibrium point is globally asymptotically stable. Under specific circumstances, the food chain system experiences a transcritical bifurcation around the axial and border equilibrium points. However, under some conditions, a Hopf bifurcation happens around the border equilibrium point.