Dynamics of the predator-prey system with double Allee effects for the prey

摘要

In this paper, the dynamics of the predator-prey systems, with and without the double Allee effects which occur simultaneously in the same population, are studied. Analysis of the behavior of this model is carried out on two fronts—examining the local stability conditions of these equilibria and conducting extensive numerical simulations. The results show that the double Allee effects may be a stabilizing or a destabilizing force in predator-prey systems. A conclusion drawn is that the structure of bifurcation diagram may be complicated or alleviated by Allee effects. It is also pointed out that the Allee effects have different influence on the chaos. The importance of this research is to give people a better understanding of the mechanisms (Allee effects) of the natural populations.