Stability And Hopf Bifurcation For The Modle Of Turmour Growth With Time Delay

Cancer has become one of the major diseases threatening human life, using themathematical method to abstract the mathematical model of tumor growth process.We use mathematical method to analyze dynamic character of tumor growth. It canprovide theoretical basis for tumor control.This paper has studied the mechanism of the process of tumor growth whichitself has a carrying capacity and the important role of angiogenesis in tumor growth.We have mainly studied a class of tumor growth models with time delay. Firstly, thispaper has studied the stability of the equilibrium point of the system, and discussesthe existence of positive equilibrium conditions, focuses on the positive equilibriumkinetic properties, including positive equilibrium stability and existence of Hopfbifurcation and so on. This paper studies the case of a single delay. By analyzing thedistribution of characteristic equation root, we have draw the conclusions that thesystem is asymptotic stability of equilibria and the existence conditions of Hopfbranch.Secondly, using the theorem and the theory of shape center popular analysesthe direction of Hopf branch and the stability of periodic solutions.Finally, based on the results of theoretical derivation, we give concretenumerical value and use mathematical software Matlab to analysis the numericalsimulation of the image, so as to validate the correctness of the theoretical analysis.