Qualitative Analysis About A Predator-prey Model With Allee Effect And More Time Delays

In this paper,a predator-prey system with Holling ? and Allee effect is considered,which has more time delays and prey has Allee effect.The reasonable extension and improvement of the system has been made based on the actual situation the corresponding model in the recent literature.In the first chapter,the research background and the work of the previous scholars are introduced.In the second chapter,for the system without time delay,the existence of all boundary equilibria and a positive equilibrium are analyzed,and then the sufficient conditions for the local stability of the equilibrium point and global stability of positive equilibrium are obtained.In the third chapter,for the system with time delays,first the invariance and boundedness of the system solution are discussed,the sustainability of the system is also discussed,then the sufficient conditions for the local stability and global stability of positive equilibrium are obtained by constructing suitable Lyapunov functionals,finally,the sufficient condition of Hopf bifurcation point of the system is studied by analyzing the positive equilibrium of the characteristic equation.Meanwhile,some examples are presented to illustrate these results by Matlab numerical simulations.