Dynamical Analysis Of A Type Of Stage-structured Predator-prey Models

In this paper, we consider stage-structured predator-prey models with general functional response of predator and with prey using hawk and dove tactics. The paper consists of three parts, in the fist two of which the resources that are suppled for predator and prey are assumed to be aboundant. In chapter 1, a stage-structured predator-prey model with general functional response is studied. We consider immature and mature individuals of the prey population are divided by a fixed age and the predator individuals only prey on the immature prey individuals. We show that a supercritical Hopf bifurcation will occur under some conditions by using the density dependent rate in immature prey population as bifurcation parameter. Sufficient conditions which guarantee the uniform persistence and global stability of boundary equilibrium are also obtained. These conclusions are in general settings and are suitable for predator-prey models with Holling type-II, Holling type-III, Rosenzweig and lvlev functional response. Futhermore, numerical simulations are presented to illustrate these results.In chapter 2, a ratio-dependent predator-prey model with stage structure for the prey is studied. We also assume that predator individuals only prey on the immature prey individuals. Existence of equilibria is discussed and their local asymptotical stability is analyzed by linearization and system transforming since the system can't be linearized at the origin. We find the trivial equilibrium is always unstable, which implies that the system is persistent. It is shown that the system is uniformly persistent when positive equilibrium exists. And global stability of boundary equilibrium, which implies the extinction of the predator population, is studied by the limit system theory and Dulac criterion. These conclusions are suitable for predator-prey models with Holling type-II, Holling type-III and Rosenzweig functional response. Lastly, numerical simulations are presented to illustrate these results.In chapter 3, we consider a predator-prey model with stage structure and hawk-dove tactics for the prey. It is assumed that the resources for mature preys are limited and vital for their survival and reproduction. Then they usually compete fiercely for the resources in order to survive and reproduce. We choose the classical hawk and dove game for mature preys in the model and the gains that are obtained in the competition will influence the fecundity of mature prey individuals directly. Existence and stability of equilibria and uniform persistence of the system are studied in two different existence regions for G < C and G > C. Finally we compare and explain the results of two models from biological view and discuss the effects of different behaviors for mature prey individuals on traditional stage-structured predator-prey model dynamics.