Two Types Of Eco-mathematical Model Dynamical Properties

This dissertation mainly deals with dynamics of some population models by using Lyapunov function method, comparison theorem and fixed point theorem of strict-set-contraction. These dynamics contain uniformly persistence, ultimate bound, global stability and existence of positive periodic solution.The paper is composed of three chapters. In Chapter 1, the historical background and significance of the problem to be studied are introduced. Then, we summarize some excellent works which emerge in recent years. In Chapter 2, the persistence and global stability of a ratio-dependent predator-prey model with stage structure is studied by using Lyapunov function method and comparison theorem. In Chapter 3, a neutral delay predator-prey system with HollingⅡfunctional response is investigated. By using a fixed point theorem of strict-set-contraction, a new criterion is established for the existence of positive periodic solution of the system.