On The Existence Of Community In A Polluted Environment

With environment pollution being more serious, people pay close attention to existence of population with toxin gradually. It becomes hot spot problem to study the existence of population and their change law in a polluted environment. Pollution and capture are two important factors which affect the existence and development of population, and capture changes with the transformation of season and population when existence space is smaller and smaller. Therefore,it has practical sense to study the existence of population under conditions that capacity is small and capture is variable. Now, the study result about single community under several existence conditions is few, and people seldom discuss single community's existence states at the same time. The research for two community only confines to two-dimensional Volterra predator-prey system and competing system. Furthermore, the discussion progresses under the conditions that capacity is large and the effect that toxin affects population by food chain is neglectful. This paper studies the existence of a kind of general Logistic population which live in a large capacity and polluted environment with capture by methods of integral in mean,comparability principle and differential inequality principle.It gives the sufficient conditions for β-persistence, β-extinction and extinction in finite time,and obtains the maximal harvesting rate when the population is β-persistence.When the capacity is small and the capture is a linear function for population,it gets the sufficient conditions for weak persistence and extinction.This makes the research in region for single community even more deeper and fuller. Using the same methods,this paper also studies the existence of two-dimensional Volterra cooperative system in a small capacity and polluted environment when toxin affects population by food chain.It obtains the sufficient conditions for weak persistence in the mean,extinction, β-persistence and β-extinction.It also gives the relational expression about parameter fluctuation and solution position,and defines the final changing range of solutions under corresponding conditions.This offers theoretical foundation for practical applications.