The Dynamics Study Of Three-species Competition Model

This paper mainly studies the existence of solutions for the three species competition models.Three species competition system is a kind of important biological competition system,which is a frontier direction of the competition theory research of biological system at present.Compared with single species or two species competition model,the three species competition model has more complex structure,which can better describe many biological phenomena.In Chapter 1,the background and main work of the three species competition models are introduced.In Chapter 2,we first study the existence of positive solutions for the three species partial competitive systems with homogeneous Neumann boundary conditions,mainly using the comparison principle and the upper and lower solution methods.Then,we ana-lyze the existence and stability of the positive constant equilibrium solution of the model,and give a priori estimate of the positive solution.Finally,we discuss the nonexistence of the non-constant positive solution of the model.The results show that under suitable assumptions,when the diffusion rate d1 is large,the model does not have the non constant solution.In Chapter 3,we study the three species competition model with homogeneous Dirichlet boundary conditions and cross diffusion terms.we prove the existence of semi-trivial and positive solutions by the method of upper and lower solution,and give the necessary con-ditions for existence.