| Mathematical models can be used to describe some biological phenomena quantitatively.Researchers turn biological problems into mathematical problems with the help of mathematical models,so as to explain or solve some problems in the ecosystem through the study of mathematical models.In this paper,the interaction model between two types of plant and sulfide in salt marsh ecosystem are studied.In Chapter 1,we mainly introduce the biological background,research significance and current situation of the feedback model between plants and sulfide in salt marsh ecosystem,the research content and relevant mathematical theory knowledge.In Chapter 2,the plant sulfide feedback model with Logistic growth is studied.Firstly,the existence and local stability of the equilibrium points are discussed.Secondly,the Lyapunov function is constructed to prove the global stability of the equilibrium points.Then,considering the space diffusion,the problem is extended to the reactiondiffusion system,and the global dynamic behavior of the constant equilibrium solutions of the system is studied.Finally,Matlab is used to simulate the obtained theory and show the global dynamic state of the system.In Chapter 3,we consider the plant-sulfide feedback model inhibited by sulfide.By analyzing the model,we obtain the existence and stability of the equilibrium points,and analyze the Hopf bifurcation when there is a unique positive equilibrium point.In the same way,the model is extended to reaction-diffusion system considering spatial diffusion.The stability and Hopf bifurcation of the constant equilibrium solution of the vi system are studied,and the conditions for the existence and non-existence of nonconstant steady state solutions are studied through the properties of the equilibrium solutions.In Chapter 4,we summarize the conclusions obtained in this paper.It also discusses the shortcomings of the article and the problems and directions that can be further explored. |
