Qualitative Analysis Of Predation Systems With Group Behavior

In ecosystems,the phenomenon of social inhabitation of biological species is widespread.Species community play an important role in the survival and development of populations,and have a positive effect on maintaining the stability of ecosystems.Therefore,this Graduation Thesis builds on the predecessors to continue to study the predation system of the population with group behavior.Firstly,a Leslie-Gower-type predation system with group defense effect and strong Allee effect was established,and the type and stability of the boundary equilibrium point of the system were determined through research,and the conditions for the stability of the internal equilibrium point of the system were given.Using the bifurcation theory analysis,it is found that when the parameters change,the internal equilibrium point of the system has a saddle node bifurcation,a Hopf bifurcation and a Bogdanov-Takens bifurcation,and the corresponding numerical simulation is given.Secondly,a predation system with group defense effect and predator cooperative hunting is established,the stability of the equilibrium point of the system and the existence of Hopf bifurcation in the system under certain parameter conditions are analyzed,and the corresponding numerical simulation is given.Finally,the predation system with both bait and predator group behavior is analyzed,and the stability of the boundary equilibrium point and the existence of transcritical bifurcation and Hopf bifurcation in the system under certain parameter conditions are obtained,and numerical simulation results are given.