From mating difficulty in prey to oscillations in both prey and predator populations: Bifurcations of a predator-prey system

Abstract

We study the dynamics of a Leslie type predator-prey model with weak Allee effect in prey and Holling type IV functional response function, where the weak Allee effect arises from the difficulty in mating. We investigate the high degenerate bifurcations, including cusp type degenerate Bogdanov-Takens bifurcation of codimension 3, and focus type degenerate Bogdanov-Takens bifurcation of codimensions 3 and 4. The complicated dynamics of the system shows that weak Allee effect in prey might induce multiple steady states after some special predation interactions, and it also yields population oscillations. Furthermore, the cyclic amplitudes are sensitive on both parameters and initial values. Simulations also exhibit the qualitative results numerically.