Stability And Bifurcation Analysis Of Hunting Cooperative Predator-Prey Diffusion Model

In this thesis,the dynamic behavior of a diffusive Holling type II predator-prey model with hunting cooperation is studied.For the local model,the stability of nonnegative equilibria,the detailed behaviour of Hopf bifurcation,saddle-node bifurcation,and Bogdanov-Takens bifurcation are investigated.It is shown that under suitable conditions the model exhibits a supercritical and orbitally asymptot-ically stable limit cycle when the predator cooperation in hunting rate pass through a threshold value.For the reaction-diffusion model,we analyse the diffusion-driven Turing instability of both the positive equilibria and the bifurcating periodic so-lutions,the existence and direction of Hopf bifurcations,and the stability of the bifurcating periodic solutions which describe the spatiotemporal pattern formation-s.Our result shows that the hunting cooperation plays a crucial role in determining the stability and bifurcation behavior to the model,that is,it is beneficial to the coexistence of predator and prey,it can have a destabilizing effect,it can induce the bi-stability phenomenon,it can undergo not only the saddle-node bifurcation but also Bogdanov-Takens bifurcation,and it can induce the rise of Turing instability,which is a strong contrast to the case without hunting cooperation.Moreover,some numerical simulations are performed to visualize the complex dynamic behavior.