Stochastic Dynamic Behavior Of Tumor Growth Model Perturbed By Nonlinear Noise

With an increasing number of tumor patients in today’s world,tumor cell research has become a hot topic.Tumor growth is characterized by complex stochastic fluctuations.In theoretical studies,noise is commonly used to characterize these stochastic fluctuations.Using the knowledge of nonlinear dynamics,this dissertation investigates the steady-state and transient properties of tumor cell populations in the process of reproduction and death described by the improved Gompertz model and Richards model driven by noise.The specific research content is as follows:In the first part,the dynamic behavior of the improved Gompertz tumor cell growth system driven by associated Gaussian noise is studied.Based on the Langevin equation and Fokker-Planck equation,the effects of system parameters and noise parameters on the steadystate probability distribution curve are analyzed.The results showed that large multiplicative and additive noise intensities could reduce the total number of tumor cells and even render them extinct,inhibiting tumor cell growth.On the other hand,the noise correlation intensity reflects the synergistic effect of noise correlation factors in tumor reproduction ability.The increase of the noise correlation intensity can rapidly increase the number of tumor cells.In the second part,the dynamic behavior of the Richards tumor growth system under the excitation of non-Gaussian noise and Gaussian colored noise was studied,and the mean first passage time of the system was obtained using the fastest descent method,to measure the time required for tumor cells to reach a stable state.The results showed that the presence of non-Gaussian noise harmed the proliferation of tumor cells,and even made tumor cells endangered,while the intensity of the association between noise played a positive role in the growth of tumor cells,indicating that noise association memory had a promoting effect on the growth of tumor cells.In conclusion,the two types of tumor cell growth models studied in this dissertation enrich the dynamic properties of stochastic population systems,reveal the effects of nonGaussian noise and Gaussian noise on tumor cell population systems,and have guiding significance for effective suppression and treatment of tumor diseases.