Dynamic Analysis Of Two Classes Of Ecosystems

In this paper,we mainly study the dynamics of two classes of ecological models.The article includes three chapters.The preface is in chapter 1,we introduce the research background and the main work of this article,as well as some preliminary knowledge.In Chapter 2,A mathematical model about the interaction of two enterprises is set up and studied,and we analyzes the effect of the system with delay.First,the existence of unique positive equilibrium point of the model is proved.Second,by choosing delay ? as bifurcation parameter,found in certain conditions when ? passes through a series of critical values Hopf bifurcation will emerge.Further the conditions for the properties of the bifurcation direction,stability and periodic solution is obtained through standard theory of poincare and the central mainifold theory.Finally,some numerical simulation are provided to support our theoretical results.In Chapter 3,The dynamic behavior of an SEIR epidemic model with saturated incidence rate and saturation recovery rate is studied.Firstly,we proved that there are two kinds of equilibrium points,namely,disease-free and endemic equilibrium.Secondly,it is proved that the backward bifurcation can lead to the emergence of bistability,and the global dynamic behavior is proved by the second additive compound matrix and geometric method.Finally,simple conclusion is provided.