Dynamics of a predator-prey model with strong Allee effect and nonconstant mortality rate

Abstract

In this paper, dynamics analysis for a predator-prey model with strong Allee effect and nonconstant mortality rate are taken into account. We systematically studied the existence and stability of the equilibria, and detailedly analyzed various bifurcations, including transcritical, saddle-node, Hopf and Bogdanov-Takens bifurcation. In addition, the theoretical results are verified by numerical simulations. The results indicate that when the mortality is large, the nonconstant death rate can be approximated to a constant value. However, it cannot be considered constant under small mortality rate conditions. Unlike the extinction of species for the constant mortality, the nonconstant mortality may result in the coexistence of prey and predator for the predator-prey model with Allee effect.