A Class Of Eco-mathematical Model Of The Asymptotic Nature

This paper investgates the asymptotic behavior of three kinds of models. Model1 is a predator-prey system with functional reaction function X^1/2, By constructingthe ultimately bounded domain and Lyapunuov funtion, some result concerning per-manence are obtained. Model 2 is a nonautonomous Schoner system with feedback controls. It also considers the system have unique strictly positive periodic solution which is globally stable if it is a periodic system. Model 3 is a model with stage struc-ture and cannibalism, where the species-x has two stages, a immature stage and a mature stage, the growth of the species-y is of Lotka-Volterra nature, are modeled by a system of two retarded functure species-x prey on the immature species-x, while the mature species-x and species-y are competitive each other. We obtain the conditions for globally asymptotic stability of three nonnegative equilibria. In partitular, to our knowledge, the common effect of stage structure and cannibalism of the population on dynamical behavior are not considered. This part is also a key piont of this paper.