Study On The Dynamic Behaviors Of A Class Of Oregonator Models

In the field of partial differential equations,Bifurcation phenomenon is a very important nonlinear phenomenon.This phenomenon reflects that the topological structure of the system changes qualitatively when the parameters of the system change.For the branching problem,In this paper,a non-degenerate reaction-diffusion Oreganator model with homogeneous Neumann boundary conditions is taken as the research object.By using abstract Hopf bifurcation theorem,abstract steady-state bifurcation theorem,maximum principle and comparison principle,and using Harnack inequality and Gronwall inequality,the existence of Hopf bifurcation and steady-state bifurcation of the non-degenerate react-diffusion Oregonator model and the corresponding shadow systems were analyzed.The specific research content is as follows:Firstly,the existence of Hopf bifurcation points is determined by using abstract Hopf bifurcation theorem to analyze the non-degenerate reaction-diffusion Oregonator model.Then the bifurcation direction of homogeneous Hopf bifurcation in space and the stability of periodic solutions are analyzed.Secondly,by using the abstract steady-state bifurcation theorem to analyze the non-degenerate reaction-diffusion Oregonator model,the existence of steady-state bifurcation points is determined.At the same time,numerical simulation is used to verify the above results.Finally,by analyzing the shadow system of Oregonator model,The existence of spatial homogeneous Hopf bifurcation points and steady-state bifurcation points are determined.At the same time,the nonexistence of spatial non-homogeneous Hopf bifurcation point is also analyzed.To some extent,the results obtained in the thesis,will allow for the clearer understanding of the dynamics of this class of reaction diffusion Oregonator model.