Permanence And Extinction Of Non-autonomous Two Species Systems In A Polluted Environment

In recent years, the environmental question is more and more serious for biologicalpopulation and human. It causes more attention to people in the real world. Sincenon-autonomous system is more close to the real nature and has a strong biologicalsignificance, in this paper we establish a non-autonomous competition model andnon-autonomous predator-prey models with impulsive perturbations in a pollutedenvironment and investigate the dynamics of such systems.First, we introduce the research background.In Chapter1, for the competition population we set up a non-autonomous competitionmodel in a polluted environment with pulse pollution input and impulsive perturbations. Byusing the analytical method and comparison theorem of impulsive differential equation, wegive the sufficient conditions of permanence and extinction of the given model. Byconstructing Lyapumov function, the global attractive conditions are obtained. These resultsprovide theoretical basis for the competition population living in the polluted environmentwith discontinuous perturbations by people.In Chapter2, since most species exist in the form of prey and predator, we set anon-autonomous predator-prey model with discontinuous perturbations in a pollutedenvironment with pulse pollution input. By analyzing the predator and prey and usingcomparison theorem of impulsive differential equation, we get the sufficient conditions ofpermanence and extinction of the population. Further, we get the global attractive conditionsby constructing Lyapumov function.In Chapter3, we consider a specific predator-prey system, that is, predator-prey systemwith Holling II functional response. We obtain the sufficient conditions of permanence andextinction of population. Because these depend on the concentration of the environmentalpollution strictly, the population will tend to be extinct if the emission of pollutants isexcessive. So in order to prevent population from extinction we should control the amount ofthe pollutant emission.