Dynamics Analysis Of A Chemical Reaction-diffusion Model Subject To Degn-Harrison Reaction Scheme

A chemical reaction-diffusion model with Degn-Harrison reaction scheme and sub-ject to homogeneous Neumann boundary condition is revisited in this article.Local asymptotic stability,Turing instability and existence of Hopf bifurcation for the only constant positive equilibrium solution are established by analyzing the relevant eigenvalue problem.In particular,a simplified explicit formula determining the prop-erties of spatially homogeneous Hopf bifurcation is derived by employing the normal form method and the center manifold theorem for reaction-diffusion equations.Our formula here simplifies the existing one obtained in Dong et al.(2017).Numerical approximations are also carried out in order to check our theoretical predictions.The research work of this paper is divided into the following four chapters:In Chapter One,the background,significance and current situation of Degn-Harrison reaction-diffusion chemical model are briefly introduced,and the main research con-tents and results of this paper are pointed out.In Chapter Two,the ODE system corresponding to Degn-Harrison reaction-diffusion chemical model is considered and the stability and Hopf bifurcation of the positive e-quilibrium point are analyzed as well as the direction of the Hopf bifurcation and the stability of the bifurcating periodic solution are also discussed.Numerical simulations are included to verify the obtained theoretical results by using the Matlab soft pack-age and the numerical methods solving initial value problems of ordinary differential equations.In Chapter Three,by using the linearization method and analyzing in detail the dis-tribution in the complex plane of the eigenvalues of the associated eigenvalue problem,the local asymptotic stability and Turing instability of the constant solution of the model are studied.In order to verify the theoretical conclusions obtained,the Matlab software package is used to give appropriate numerical verification for some specific examples.In Chapter Four,Hopf bifurcation of Degn-Harrison reaction-diffusion chemical mod-el is considered and the direction of Hopf bifurcation as well as the stability of bifur-cation periodic solutions are also discussed.By choosing c as bifurcation parameter,the Hopf bifurcation value of Degn-Harrison reaction-diffusion chemical model is found by using Hopf bifurcation principle.Using the normal form theory and center mani-fold theorem,the stability and the direction of bifurcation periodic solutions of spatial homogeneous and spatial inhomogeneous of reaction-diffusion chemical model are ob-tained.Numerical approximations are also carried out in order to check our theoretical predictions.