Mathematical Model for population dynamics with Allee effect

Allee effect is a crucial phenomenon that has been studied with respect to extinction and drawn considerable attention from ecologists. Here, we study the discrete-time system with Allee effect. We demonstrate that the Allee effect alone maybe stabilizing force on single-species population, and the number of stable states decrease as the Allee effect becomes stronger in the discrete-time predator-prey system. The stabilizing force of double Allee effects that caused by cooperate antipredator behavior and mate-finding which act simultaneously upon single population is also discussed. Our results show that dynamics of population is quite sensitive to initial conditions where small changes may result in large changes in the stable states of population. These different and interesting influences of Allee effect are studied by existence and stability analysis of the equilibriums and numerical simulations.