Dynamical Behavior Study Of Two Kinds Of Mathematical Models

In this paper,we mainly study dynamical behavior of Two kinds of Mathematical Models.The paper can be divided into five chaptersIn the first chapter.,we introduce the background.,the current situation of the two kinds of models,the structure arrangement and research results about this paperIn the second chapter,we mainly introduce the preliminary knowledgeIn the third chapter,we mainly study the dynamic behavior for the well-known Gierer-Meinhard model.We study the system parameters influencing on the stability of equilibrium.First.,We discuss the conditions on the stability and instability of the equilibrium point.Then,in the case of stability,we seek for the attract domain;While in the case of instability,we will prove the existence of limit cycle.We claim that the occurrence of Hopf bifurcation in the critical case.Graphs are also used to illustrate our theoretic results.In the fourth chapter,we mainly study the dynamic behavior for a model of poly-merization.Moreover,we study the dynamical behavior in the equilibrium point of three models.When the parameters are changed,different phenomena will appear,and the similarities and differences of the three models will be comparedThe last chapter is a conclusion and outlook.We summarize the thesis and give some open problems.