The Global Attactivity For Three Types Of Ecologic Modles And The Oscillation For One Kind Of Logistic Model

Global attractive for ecological mathematics models is an important research subject. In real environments, the factors that affect the variation of population density are many-sided and the relations are diversified and complicated. Some parameters' variation of ecological models will cause the variation of population's stability, which need be controlled to keep the balance of local environment. In this paper, the global attractivity is investigated firstly, which includes the existence and stability of positive trivial solution, the attractivity of positive solution, etc. Second, the oscillation of a type of single ecological model is studied.Generally speaking, the variation of population density is very complicated. It is related not only the density at the present moment but also the density at some previous moment. Moreover, the relations among them are the age distribution, the sex rate and the influence of environment, etc. In chapter 2, a multi-delay feedback control Logistic model is studied. By constructing Lyapunov-type functional and using differential inequalities, the sufficient conditions for the model are got.Ecological systems and their parameters in real world are affected by season variation, food's increase and decrease and the habit of animals' pregnancy, etc. Moreover, they don't all vary periodically. For the sake of approaching real phenomenon, in chapter 3, piecewise constant arguments sequence function in the feedback control is induct to study a multi-delay feedback control system with piecewise constant arguments. By constructing assistant system and Lyapunov function, the sufficient condition of global attractivity is got.The competitive ability of ecological population during their immature, mature and senescent stages is always changing. Even in different life stage, the demanding and viability of species is different. Furthermore, environmental pollution earthquake and so on have affected the viability of population. Moreover, the competition among...