To Study The Effect Of Diffusion Rate And Interspecific Competition Coefficient On Ecological Behavior Of Species In Lotka-Volterra Model

From the view point of the partial differential equations,the semilinear parabolic equation is called the reaction diffusion equations.In the mathematical theory,the reaction diffusion equation is mainly to consider the behavior of the solution with any initial and boundary value conditions as time changes.For example,the existence and uniqueness of global solution?fluctuation?tending to balance and the structure?stability?bifurcation phenomena of equilibrium solution and so on.In recent years,Lotka-Volterra competition diffusion model extensively studied by mathematicians and biologists.For a long time,scholars mainly study the interspecific competition coefficient?diffusion rate?space of the Lotka-Volterra competition model and so on,and have got many interesting results.In this paper,we mainly study the interspecific competition coefficient and the diffusion rates dependent of the space in the Lotka-Volterra competition diffusion model.Based on the previous studies,the interspecific competition coefficients are expanded.Using the Shadow System when the internal competition coefficient is 1 to the range of(0,1),which is same to consider the two competing species steady state.The final steady state result of internal competition coefficient is the range of(0,1)which is same with internal competition coefficient is 1.We use the principal eigenvalue method to study the population dynamics of each species whose diffusion rate dependent of the space location.The conclusion is similar to the diffusion rates independent of the space location.The main results of this paper are as the following:1.In the chapter 1,the paper mainly introduce the background,purpose and meaning of the research on the Lotka-Volterra competition diffusion model.2.In the chapter 2,the paper will introduce Shadow System and some basic concepts and theorems on principle eigenvalues in Lotka-Volterra competition diffusion model.3.In the chapter 3,the paper mainly summarize some conclusions of interspecific competition coefficient in Lotka-Volterra competition diffusion model.We will prove some basic theorems of Shadow System and use these theorems to consider the steady state of Shadow System and then that of the original system.4.In the chapter 4,the paper introduce some relevant conclusions when the diffusion rates don't depend on the space location.We conclude that there are similar dynamic behavior whether the diffusion rates depend on the space or not.5.In the chapter 5,the paper summarize our results and talk about the future research work.