Studies On Three Types Of Stage-Structure Population Dynamics System And The Hopf Bifurcati On Of A Predation System

In previous work, the great survival capability of different species among different life stage was always ignored, and the species were always supposed to admit the identical competitive ability during their immature, mature and senescent stages. However, it is not true, because the viability of population is often closely connected with the life stage that its individual belongs to. Species exhibit different characteristic during different growing processing ,and the permanence and extinction of species were influenced to differential extent. Hence, it is very significant to differentiate the differential stage structure. In this thesis, some stage-structure population dynamical models were established , and the effect of diffusion, refuse, cannibalism and impulse about the permanence, extinction and the stability were studied. In the end, the Hopf bifurcation of a class predator-prey model was studied.In chapter 2, the population dynamical systems of two species predator-prey systems with refuges and cannibalism were studied. In real world many species can be divided into two or three phases. Because short of food the immature species can be preyed by the adult species, and the immature species always try it's best to escape when being preyed. It is show that the system is uniformly persistent under some appropriate conditions, and sufficient conditions were obtained for the global stability of the positive equilibrium of the system. Further, the stability effect of cannibalish on the three stage-structured was analyzed.In chapter 3, a two-species predator-prey stage structure population dynamical system with dispersal was investigated. Transplant is a general phenomenon among population growth. Population can dispersal from one region to another area when this area no longer suits for their existence. Both of the two species have dispersal, and the dispersal capability is different among differential growing structure. It shown that the sufficient condition of the unique positive equilibrium was asymptotic stability by construction of Lyapunov function. In the following, by using the comparison theorem, we obtained the sufficient conditions for the global asymptotic stability of the positive equilibrium.The purpose of chapter 4 was to study a class pest-natural enemy model with stage structure. In real world, many people possess birth impulsive and the capture action of some reproducible resource also has the character especially kill pest by use the insecticide. In this chapter we introduce pesticides to kill pest in the predator-prey model to analyze the impulsive control strategies.