Global Analysis Of Some Types Of Predator-prey Model With Stage-structure

In this paper,the global dynamics of some types of predator-prey models for the predator or the prey with the stage structure are analyzed.The main contents are as follows:In the first place,two single population models with stage structure are established.For the two models,the existence of equilibria and their global stability are proved,Further,the basic reproduction number and other meaningful data are all determined.Secondly,a predator-prey model with stage structure for the predator is established by assuming that the benefit of predation is to increasing the growth of adult predator.And the existence of equilibria and their global stability are studied.Further,the basic reproduction number of predator,the threshold of net growth rate of prey and predation rate are obtained,they determine the global dynamics of this model,the net growth rate and the threshold of predation are all determined.Third,a predator-prey model with stage structure is established for the predator population in the presence of prey population.And its global state is analyzed,the LaSalle invariant set principle and Lyapunov direct method are used to analyse the global stability of equilibrium in the predator-prey model,and compare with the content discussed earlier,the basic reproduction number and the threshold of predation are all determined.Fourth,we establish a type of predator-prey model with stage structure for the prey and analyse the situation that the presence of a predator prey model by the equilibrium point of the existence and global stability,and determine the prey population dynamics model decides the basic reproduction threshold and the number of prey extinction or predation rate.