Analysis Of Stability And Bifurcation To Degn-Harrison System With Time Delay

This thesis investigates mainly the Degn-Harrison system with a single time delay.First of all,in the absence of delay,the stability of the positive equilibrium point and the existence of Hopf bifurcation are analyzed.Then,the effect of the time delay on the dynamical behaviors of the model is studied.The research results show that under the condition that the positive equilibrium of the corresponding ordinary differential system is stable,the increase of the delay leads to that the stable equilibrium will become unstable(that is,a single stability switch occurs).Finally,an explicit formula determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions is obtained in virtue of the central manifold theorem and the normal form method for delayed differential equations.In order to verify the correctness of the theoretical results,a numerical simulation of the obtained theoretical results was carried out.The content and structure of this thesis:The first chapter introduces the research status of the chemical model with DegnHarrison reaction format,as well as the purpose and research content of this thesis.The second chapter analyzes the stability of the positive equilibrium and the existence of the Hopf bifurcation when the delay is omitted.The third chapter studies the Degn-Harrison system with a single time delay.Chapter 4 discusses the direction of Hopf bifurcation obtained in Chapter 3 and the stability of the bifurcating periodic solutions.Chapter 5 carries out the numerical simulation to verify the correctness of the obtained theoretical results.