Coexistence Of Two Types Of Biological Analysis Of The Model

With the progress of the era, much more real problems can be solved by math-ermatization. The application value of reaction diffusion equations in the mathe-matical model in particular in the biological model has been greatly reflected. In the past twenty years, the study of reaction diffusion equation and the application of reaction diffusion equation with diffusion as the the ecologly, chemistry has been made considerable progress.In the paper, we mainly study two kinds of biological dynamics model, a predator-prey model with a Holling-Tanner reaction and a diffusive ratio-dependent prey-predator model. Based on the main use of nonlinear analysis and nonlinear partial differential equations and on the basis of previous studies, especially learn-ing from the theory of parabolic equation method and the corresponding elliptic equation, the following two specific biological model has been studied: The discussion includes priori estimates for positive solutions, stability, existence of positive solution, bifurcation and so on.In the first chapter, we mainly introduce the effect of reaction diffusion equa-tions in solving practical problems and cross in other subjects, as well as several kinds of prey-predator models.In the second chapter, a prey-predator model with Holling-Tanner reaction (0.1) is studied. By degree theory and characteristics, we mainly study the stability of the equilibrium state of the model and the coexistence of the existence of the solution in certain conditions. The condition for coexistence solutions is given.In chapter3, we study a diffusive ratio-dependent prey-predator model (0.2). The method is bifurcation theory and reliability theory. Taking d2as the bifurcation parameter, we study the bifurcation at positive constant equilibrium by means of the bifurcation theory and the Leray-Schauder degree theory. Then the local bifurcation which can be extended to the global bifurcation is proved and the fact that the global bifurcation joins up with infinity in the case of one-dimension is obtained.