The Survival Analysis Of Leslie System In The Polluted Environment And The Periodic Solutions And Asymptotic Stability Of The Volterra Equation

In this paper, there are three parts. The first part concentrates on the study of the effect of toxicant for the consumer population in a Leslie system in polluted enviroment. We use comparison theorem and a new method to analysis the problem of persistence and extinction. Some conditions for weakly Persistence and extinction are obtained;In the second part, we respectively use C_h space and C_g space theorem to study the existence of periodic solutions of Lotka-Volterra equation with infinite delay, in the end we get the condition of the existense of periodic solutions and estimate the interzone of it. In the third part, we study the asymptotic stability of a class of convolution liner Volterra stochastic integro-differential systems. By constructing suitable Lyapunov functions, we establish sufficient criteria for asymptotic stability of the zero solutions.The tree of this article as follows: In introduction, we focus on the background and value of the subject;In chapter one, we analysis the persistence of Leslie system in a polluted enviroment;In chapter two, we study the periodic solutions of Lotka-Volterra equation with infinite delay. In chipter three, we study he asymptotic stability of a class of convolution liner Volterra stochastic integro-differential systems.