The Qualitative Properties For Some Type Of Population Models

Population dynamics is an important branch of biological mathematics.We usually formulate population models by means of mathematical modeling.Some ecological phenomena are explained to study the law of life science.In this thesis,we take population models as research objects.we discuss dynamic properties of a class of nonlinear impulsive delay Nicholson’s blowflies models and delay predator-prey models.The main contents of this paper are summarized as follows : Firstly,we discuss a class of nonlinear impulsive delay Nicholson’s blowflies models.Sufficient conditions are obtained which guarantee the uniform persistence and the existence of positive periodic solutions for the model based on the comparison principle.By using the coincidence degree theory,some sufficient conditions are determined that guarantee the existence of positive periodic solutions for the model.Secondly,we investigate the dynamic behaviour for a class of nonautonomous density-dependent delay predator-prey models.The sufficient condition that guarantee the uniform persistence is reached by using the comparison principle.By using Lyapunov function,we analyze that the model is globally attractive and the uniqueness of positive periodic solution for the system.