Does mutual interference stabilize prey–predator model with Bazykin–Crowley–Martin trophic function?

Abstract

We investigated a system of ordinary differential equations that describes the dynamics of prey and predator populations, taking into account the Allee effect affecting the reproduction of the predator population, and mutual interference amongst predators, which is modeled with the Bazykin–Crowley–Martin (BCM) trophic function. Bifurcation analysis revealed a rich spectrum of bifurcations occurring in the system. In particular, analytical conditions for the saddle–node, Hopf, cusp, and Bogdanov–Takens bifurcations were derived for the model parameters, quantifying the strength of the predator interference, the Allee effect, and the predation efficiency. Numerical simulations verify and illustrate the analytical findings. The main purpose of the study was to test whether the mutual interference in the model with BCM trophic function provides a stabilizing or destabilizing effect on the system dynamics. The obtained results suggest that the model demonstrates qualitatively the same pattern concerning varying the interference strength as other predator-dependent models: both low and very high interference levels increase the risk of predator extinction, while moderate interference has a favorable effect on the stability and resilience of the prey–predator system.