Dynamic Complexities In Discrete-time Predator-prey System With Allee Effect In The Prey

With the destruction of natural environment becoming more and more serious, the extinction rate of biological population is faster and faster, the recycling of various resources has also attracted many scientists' attention to serious thinking. More and more scientist put a lot attention to the Allee effect. In this paper, we will use bifurcation center manifold theorem and bifurcation theory to study the stability of equilibrium and the bifurcation of the discrete predator-prey system with Allce effect in detail. By calculatig, we obtain the conditions of Flip bifurcation and Hopf bifurcation in the system, then we use the Matlab program to simulate the picture and give the relevant conclusions and biological significance.