Homotopy Analysis Solution Of Reaction-Diffusion Systems

The reaction diffusion system is widely used in the fields of biology, physics,chemistry, ecology and control engineering. Its mathematical model and solving method has been a hot issue of people’s attention, and it has got many valuable results. However, due to the complexity of the nonlinear system, the dynamic behavior of the nonlinear system is still to be further studied.In this paper, the background of the reaction diffusion system and the development trends of the domestic and international developments are introduced.On this basis, the one-dimensional reaction diffusion model is studied by means of the combination of spatial difference and time homotopy, and the structure of its solution is given. This method applies to typical Burgers-Huxley definite problem,and the result show that the method is feasible and effective for solving the problem of the one-dimensional reaction diffusion. In the same way, the structure of the solution of the two-dimensional reaction diffusion model is obtained and applied to the typical Brusselator definite problem. The results show that the method is feasible and effective.This article is divided into five chapters. In the first chapter, it introduces the historical background, the research significance and the development trends of domestic and international of the reaction diffusion systems, and briefly introduces the work of this paper. In the second chapter, it presents the analysis and reviews of the difference method and homotopy analysis method, and the significance and influence of the methods. In the third chapter, we obtained the structure of the solution of one-dimensional reaction diffusion model by using the method of the combination of differential method and homotopy analysis method. We verified an instance validation of an example of the typical Burgers-Huxley problem, and analyze the structure of the final analytical solution. It shows that the method is feasible and effective in solving the problems of one-dimensional reaction diffusion model. In the fourth chapter, we obtained the structure of the solution of two-dimensional reaction diffusion model by using the method of the combination of differential method and homotopy analysis method. We verified an instance validation of the typical two-dimensional reaction diffusion model Brusselator model, and analyze the structure of the final analytical solution. It indicates that themethod is feasible and effective. The last chapter makes a summary and discussion of the full text of the study. The results of the research show that this method is feasible and effective for solving the reaction diffusion systems, and it is of great significance.