Several Types Of Eco-mathematical Model Of Cycle Solution And A Lasting,

The persistence, existence, stability and global attractivity of periodic or almost periodic solutions of competition-predator systems are an important direction of mathematical ecology research. This dissertation mainly deals with dynamics of some population models by using Lyapunov function method and comparison theorem of ordinary differential equations, the basic theory of impulsive differential equations, contituation theorem of coincidence degree theory. The paper is composed of six chapters.In chapter 1, the historical background of problems to be studied and the significance of this dissertation are introduced. We summarize some excellent works in population dynamics. Then, we introduce some excellent works which emerge in recent years.In chapter 2, the persistence for a nonautonomous predater-prey system with ratio-dependence and time delay is considered, and sufficient conditions for the persistence of the system are obtained. Also, when the system is periodic, some sufficient conditions for the existence and global asymptotic stability of a positive periodic solution of the system are given.In chapter 3, a nonautonomous predater-prey periodic system with ratio-dependence is discussed, and time delay is also consided during the process of the functional response. By using a continuation theorem based on coincidence degree theory, we study the global existence of positive periodic solution. A set of easily verifiable sufficient conditions are obtained.In chapter 4, a class of nonautonomous Volterra systems with feed-back control and Holling-Ⅱfunctional response is investigated, and the time delay phenomenon is also considered during the process of the functional response. The sufficient conditions for the uniforn persistence of the system are proposed by constructing appropriate Lyapunov functions, and a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of the model. Moreover if the system is periodic, the existence of the positive solution is proved by the Brouwer's fixed point theorem.In chapter 5, a nonautonomous dispersal prey-competition system with pure-delays is investigated. By using a comparison theorem and delay differential equation basic theory, we obtain sufficient conditions for the permanence of the population in every patch. By constrcting suitable Lyapunov functionals and using almost periodic functional basic theory, we prove that the system is globally asymptotically stable and has a unique almost periodic solution under some appropriate conditions.In chapter 6, a nonautonomous dispersal competition system with impulsive effect and time delays is investigated. By using the continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are obtained to guarantee the existence, uniqueness and glabal stability of positive periodic solutions of the system.