Does mutual interference stabilize prey-predator model with Bazykin-Crowley-Martin trophic function? (Q6566676)

The authors investigate a 2-dimensional predator-prey ODE model with Bazykin-Crowley-Martin (BCM) functional response and strong Allee effects for the predator population, being assumed that in the absence of the predator the prey obeys a logistic growth law. The purpose of choosing a BCM functional response is to precisely quantify the effects of the interferences between predators upon the dynamics of the system, being observed that moderate levels of interference have a stabilizing effect, while both high and low levels lead to predator extinction.\N\NDue to the occurrence of the Allee effects, it is seen via a detailed analysis of the isoclines that the prey-only equilibrium has a nonempty basin of attraction and the model can have up to six equilibria. The stability of the interior equilibria is discussed, conditions for the occurrence of saddle node, Hopf, cusp and Bogdanov-Takens bifurcations, respectively, being determined. Numerical simulations are then performed to illustrate the analytical findings, confirming the fact that the stability and resilience of the predator population heavily depend upon the level of predator interference.