Dynamic Behavior Of An Ivlev Functional Reaction Predator-prey Model With Double Allee Effects

In this thesis,we study the dynamic behavior of an Ivlev type predator-prey model with double Allee effects.For the local model,we first analyze the stability of nonnegative equilibria and the detailed behavior of the Hopf bifurcation generated at a positive equilibrium point.The results show that under certain conditions,the double Allee effects change the stable interval of the positive equilibrium point,has a destabilization on the model,and at the positive equilibrium point,the model undergoes a supercritical Hopf bifurcation and the bifurcating periodic solution is asymptotically stable;Then,through numerical simulation and comparative analysis of the effect of different parameters on the stability of the positive equilibrium point,it can be seen that the number of predator gradually decreases as the difficulty of finding a mate gradually increases;Finally,the existence of limit cycle is proved.For the self-diffusion model,the stability of the positive equilibrium point and the existence of the Hopf bifurcation are analyzed,and the conclusions are verified by numerical simulation.It is obtained that self-diffusion does not lead to Turing instability,and the Hopf bifurcation is supercritical,and the bifurcating periodic solution is orbitally asymptotically stable on the central manifold;For the crossdiffusion model,it is find that cross-diffusion can cause Turing instability.The spatial pattern will appear and be verified by numerical simulation.