Dynamics Of Several Biomathematics Models

This thesis mainly deals with dynamics of three types of population models by applying Lyapunov function method and comparison theorem of functional differential equations, continuation theorem of coincidence degree theory, a fixed point theorem of strict-set-contractions, a fixed point theorem of cone and some analysis techniques. These dynamics properties including:persistence, existence and uniqueness of periodic solutions, stability of periodic solutions.The organization of this thesis is as follows. This paper is composed of four chapters.In Chapter1, we introduce the preliminary which is necessary in the thesis. We also recall some backgrounds of the problems to be studied and some basic knowledge.In Chapter2, an N-Species trophic level food chain model with ratio-dependent Michaelis-Menten type functional response is investigated. Firstly, some sufficient condi-tions on the persistence for the the system is obtained by comparison theorem of functional differential equations. Secondly, some sufficient conditions on the existence of periodic so-lution for the the system is obtained by continuation theorem of coincidence degree theory.In Chapter3, we study an neutral differential system with feedback control. By applying a fixed point theorem of strict-set-contractions, some new criteria are established for the existence of positive periodic solutions this system.In Chapter4, by using a fixed point theorem of cone, sufficient conditions are obtained for the existence and global attractivity of a unique positive periodic solution for a a class of general Lasota-Wazewska-type model with periodic coefficients.