Research On Autonomy And Three Types Of Stage-structure Population Dynamics Systems

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 in previous work. 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 stage, 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 about the permanence, extinction and the stability were studied.In chapter 2, the issue of the systems of two species was studied. In chapter 3, the 2-Spieces Competitive Model was founded, by using the stability theory of the ordinary differential Equation. We make a qualitative analysis of the equilibrium points' stability of 2-species coexistence state. Then the conditions of the 2-species coexistence were gained. After that, two conditions were given and no cycle in the 2-Spieces periodic solution under those conditions was testified, then the biological explanation to the main conclusion has also been given.In chapter 4, the population dynamical systems of two species predator-prey systems with refuge and cannibalism were studied. In real world many species can be divided into two or three phases. Because of food shortage the immature species can be preyed by the adult species, and the immature species always try its best to escape when being preyed. It shows 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. Furthermore, the stability effect of cannibalish on the three stage-structured was analyzed.In chapter 5, a two-species predator-prey stage structure population dynamical system with dispersal was investigated. Transplant is a general phenomenon among population growth. Species could dispersal from one region to another area when this area is no longer suitable for their existence. Both of the two species have dispersal, and the dispersal capability is different among differential growing structure. It shows that the sufficient condition of the unique positive equilibrium was asymptotic stability by construction of Lyapunov function. As following, we obtain the sufficient conditions for the global asymptotic stability of the positive equilibrium via the comparison theorem.The purpose of chapter 6 was to study a class pest-natural enemy model with stage structure. In real word, many people possess birth impulsive and the capture action 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. We can obtain that the stable of predator -free periodic solution is existed. Furthermore, the existence of a nontrivial periodic solution was considered by using bifurcation theory when the predator was existed. Therefore, we can kill pests as many as possible with pesticide while keeping the natural enemies from extinct.