Dynamics Analysis Of A Class Of Chemical Reaction Systems With Time Delay

In this paper,the chemical model with a Degn-Harrison reaction scheme and a single discrete time delay is considered.Firstly,the stability of the positive equilibrium point and the existence of the Hopf branch of the corresponding ordinary differential equation are considered.Secondly,under the condition that the positive equilibrium of the ordinary differential equation model is stable,the stability of the positive equilibrium point and the existence of the Hopf branch under the influence of time delay are analyzed in detail,and the multiple stability switches of the positive equilibrium point are obtained.Finally,using the central manifold theorem and the canonical form method of the delay differential equations,the explicit formula for judging the direction of the Hopf bifurcation and the stability of the bifurcation periodic solution is obtained.In order to test the rationality of the conclusions obtained,the Matlab software package is used to give appropriate numerical verification for the given model.The first chapter summarizes the research background,current situation of DegnHarrison model and the main content of this paper.The second chapter considers the stability and the Hopf bifurcation problem of the positive equilibrium point of the ordinary differential equation model corresponding to the delayed Degn-Harrison model,and numerically simulates the theoretical results obtained.The third chapter studies the stability of the positive equilibrium point and the existence of the Hopf bifurcation of the Degn-Harrison model with time delay,and gives appropriate numerical simulations to the theoretical results obtained.The fourth chapter uses the central manifold theorem and canonical form of delay differential equations to calculate the explicit formula judging the direction of the Hopf bifurcation and the stability of the bifurcation periodic solution obtained in the thrid chapter.