Dynamic Behavior Analysis About Two Kinds Of Tumor Models

In this paper,we study the stability of tumor growth model under the influence of uncertainties and the dynamic characteristics of tumor-immune system under the influence of Allee effect according to the theory and method of nonlinear dynamic system.Firstly,we construct stochastic effects mathematical model about tumor growth.According to the probability distribution,the random variables are classified into Uniform distribution?Gaussian distribution and ? distribution.This random model is converted into an equivalent deterministic model based on the Chebyshev polynomial approximation.The stability of the equilibrium point of the equivalent model is analyzed by linear stability theory.Secondly,the dynamic characteristics of deterministic tumor-immune system under the influence of Allee effect are discussed.We develop a definite tumor-immune model with Allee effect,and analyze the property of deterministic model,including the positivity,boundness and local stability.And discussing the tumor-immune model with Allee effect,which disturbed by white noise.Based on the method of stochastic averaging,we obtain the expressions of the steady-state probability density and the mean first-passage time.At the same time,some numerical simulations are given to illustrate the analytic results.