一类肿瘤-免疫模型的稳定性与Hopf分支分析  

Stability and Hopf Bifurcation Analysis ofa Class of Tumor-Immune Models

作　　者：赵浛弛 李杰梅 ZHAO Hanchi;LI Jiemei(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,兰州730070

出　　处：《吉林大学学报（理学版）》2024年第2期189-196,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11801243)。

摘　　要：考虑一类肿瘤-免疫模型,讨论其平衡点的存在性条件,并利用特征方程分析各平衡点的局部动力学稳定性,证明该模型在相应条件下会发生Hopf分支.通过计算第一Lyapunov系数得出:如果系数不为零,则模型发生Hopf分岔;如果系数小于零,则分岔是超临界的;如果系数大于零,则分岔是次临界的.最后利用数值模拟验证理论分析结果.We considered a class of tumor-immune model,discussed the existence conditions of their equilibrium points,and used characteristic equations to analyze the local kinetic stability of each equilibrium point,proving that the model underwent Hopf bifurcation under the corresponding conditions.By calculating the first Lyapunov coefficient,it can be concluded that if the coefficient is not zero,the model undergoes Hopf bifurcation,the bifurcation is supercritical if the coefficient is less than zero,and the bifurcation is subcritical if the coefficient is greater than zero.Finally,numerical simulations are used to validate the theoretical analysis results.

关 键 词：肿瘤-免疫模型 稳定性 HOPF分支 超临界 次临界 

分 类 号：O175[理学—数学]