Research Of Dynamical Behaviors Of A Class Of Carcinogenesis Model

In this paper,aimed at the problem of the early cancer occurrence,we choose a class of reaction diffusion coupled carcinogenesis model as our target model.By using the linearization principle and the Hurwitz's criterion to consider the existence,stability of the non-negative equilibrium solutions of both reaction diffusion equations and the ordinary differential equations;In particular,we consider the Turing instability of the positive equilibrium solution of the reaction-diffusion equations.The main contents of the thesis are: we consider the dynamical behaviors of the early carcinogenesis model in the form of the ordinary differential equations.We study the existence and stability of the non-negative equilibrium solutions.We consider the dynamical behaviors of the early carcinogenesis model in the form of the reaction diffusion equations.We study the asymptotic stability and the instability of the non-negative equilibrium solutions;In particular,by using Hurwitz's criterion,we derive precise conditions on diffusion rates so that under these conditions the positive equilibrium solution undergoes Turing instability;Then,by using our analytical analysis,we do numerical simulations,which,to some extent,verify our analytical analysis.The analytical results obtained in the thesis will allow for the clearer understanding of the dynamic behavior of early carcinogenesis model,and will provide a theoretical basis for people to understand how to treat cancer in depth.