Stability And Branching Analysis Of A Class Of Lengyel-Epstein Systems With Time Delay

Chemical reaction is a complex process.However,the change of reactant con-centration in the actual reaction is affected by the time lag factor.In order to further study the influence of time lag on the reactant concentration change in the reaction process,this paper examines the dynamical analysis of the Lengyel-Epstein systems with a discrete delay in detail.The main contents of this paper are arranged as fol-lows:In the first chapter,the research background and current situation of Lengyel-Epstein model with discrete time delay are described.Furthermore,the main con-tents of this article are pointed out.The second chapter discusses the local asymptotic stability and the Hopf bifur-cation of the positive equilibrium of the ODE system.Under the assumption that unique positive equilibrium of the model is locally asymptotically stable in the absence of the delay,the effect of the increase of delay on the stability of the unique positive equilibrium is analyzed in detail in the third chapter.It is founded that under suitable conditions on the other parameters,the delay doesnt't affect the stability of the equilibrium,namely,the equilibrium is abso-lutely stable while under the other conditions on the other parameters,the equilibri-um will become ultimately unstable after passing through multiple stability switches and Hopf bifurcations at some certein critical values of delay.Particularly,by means of the normal form method ane the center mainfold reduction for retarded functional differential equations,the explicit formulae determining the derection of Hopf bifur-cations and the stability of the bifurcating periodic solutions are obtained.To verify our theoretical conclusions,Matlab is used for numerical simulation in the fourth chapter.