Stability And Hopf Bifurcation Analysis Of Tumor Model With Time Delay

Cancer is the leading killer of human being and has become a worldwide hot topic.In recent years,the scientists used mathematical method to analyze dynamic behavior of tumor model.The primary objective of this paper is to study the tumor growth model and tumor virotherapy model with time delay by using bifurcation theory.The major contents are as follows:First,this paper introduces the development and research situation of tumor growth and a mathematical model of tumor growth with two time delays is studied.By analyzing the distribution of the roots of the characteristic equation of the linearized system,τ₁and τ₂are chosen as the bifurcation parameters,the stability of the system is discussed.Then,we analyzed the existence of Hopf bifurcation by using bifurcation theory.Further,through the method of normal form theory and center manifold theorem,and calculation formulas for judging the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are given.At last,numerical simulations of this paper are carried out by using Software Mathematica.Second,this paper introduces the development and research situation of tumor virotherapy,using the same method,the dynamic behavior of a tumor virotherapy with two time delays is investigated.