具有非平稳参数的二维肿瘤模型的B-tipping分析  

B-Tipping Analysis of a Two-Dimensional Tumor Model with Nonstationary Parameters

作　　者：袁娅茹 邱志鹏[2] YUAN Yaru;QIU Zhipeng(School of Mathematics and Statistics,Nanjing University of Science and Technology,Nanjing 210094,China;Center for Basic Teaching and Experiment,Nanjing University of Science and Technology,Jiangyin 214443,China)

机构地区：[1]南京理工大学数学与统计学院,南京210094 [2]南京理工大学基础教学与实验中心,江苏江阴214443

出　　处：《赣南师范大学学报》2024年第3期1-7,共7页Journal of Gannan Normal University

基　　金：国家自然科学基金(12071217,12361098);江西省自然科学基金面上项目(20232BAB201024)。

摘　　要：本文建立了一个参数是非平稳变化过程的CD8+T细胞与肿瘤细胞相互作用的数学模型.首先对固定参数条件下的系统进行动力学分析,理论结果表明系统存在双稳态现象和鞍结点分岔.其后引入函数s(t)描述CD8+T细胞输入率的非平稳参数变化过程,发现系统在非平稳参数变化下存在B-tipping现象:系统轨迹随着时变参数s(t)的缓慢增加跟踪固定参数系统的轨迹,在分岔点处达到临界状态并经历突变趋向另一个稳定状态.在癌症治疗过程中,通过调节CD8+T细胞的输入率将患者状态移到tipping point可以有效地控制肿瘤生长.A mathematical model is formulated to describe the interaction between CD8+T cells and tumor cells within a non-stationary changing process.Firstly,the system undergoes dynamic analysis with fixed parameters.The theoretical results show that the system has bistable phenomena and saddle bifurcation.Then,the function s(t) is introduced to describe the non-stationary parameter change process of CD8+T cell growth rate.The result shows that the system has B-tipping phenomenon under non-stationary parameter change:The trajectory of the system follows the trajectory of the fixed parameter system as the time-varying parameter s(t)slowly increases,reaching a critical state at the bifurcation point and experiencing a sudden change toward another stable state.During cancer treatment,shifting the patient's state to a tipping point by regulating the CD8+T-cell input rate can effectively control tumor growth.

关 键 词：肿瘤模型 B-tipping point 双稳态 鞍结点 

分 类 号：O175.1[理学—数学]