Dynamic Analysis About A Three Populations Model With Modified Leslie-gower And More Time Delays

In this paper, a three populations model with modified Leslie-Gower and moretime delays is considered. For the model without time delay, the existence conditionsof the equilibrium points, the local asymptotically stability of all boundary equilibriaand the global stability of a positive equilibrium in this model are discussed. Undertime delays, the local asymptotically stability of all boundary equilibria and the localHopf bifurcation are studied; by constructing suitable Lyapunov functionals, thelocal asymptotically stability and the global stability of a positive equilibrium insystem are also discussed. Meanwhile, some examples are presented to illustratethese results by numerical simulations.