The Periodic Solutions Of An Infinite Delay Differential Equation And The Survival Or Extinction Of Population In The Polluted Environment

In this paper, we discussed some questions about mathematical ecology. The rest paper is followed as:First section is introduction which is mainly composed with some prepared work. In this section we recommend the development history of some mathematical models and a few basic conception about mathematical ecology.In the first chapter, we research the dynamics of population which were in the polluted environment, we will(l): give the corresponding mathematical model;(2): obtain the explicit conditions for the threshold of the population by means of comparison theorem.In the second chapter, we study an infinite delay differential equation, the system was widely applied in the biology, neural network and some other fields. By the coincidence degree theory and the second method of Liapunov we get the conditions for the existence of periodic solution and global attraction.