肺部免疫应答模型的稳定性分析与分支分析  

Stability and bifurcation analysis of lung immune response model

作　　者：代梦雅 张存华[1] 刘金龙 DAI Mengya;ZHANG Cunhua;LIU Jinlong(Department of Mathematics,Lanzhou Jiaotong University,Lanzhou,Gansu 730070,China;Elementary school in Dingmen Village,Tianshui,Gansu 741315,China)

机构地区：[1]兰州交通大学数学系,甘肃兰州730070 [2]丁门村小学,甘肃天水741315

出　　处：《内江师范学院学报》2024年第2期12-16,23,共6页Journal of Neijiang Normal University

基　　金：国家自然科学基金资助项目(61763024)。

摘　　要：考虑肺部感染初始先天系统反应的动态模型,首先根据三次多项式方程根的判别式,得到了模型有正平衡点的条件,其次利用平衡点稳定性理论和中心流形定理讨论了在该条件下模型正平衡点的具体类型及稳定性,最后考虑了在平衡点处出现的鞍结点分支.A dynamic model of the initial innate system response to a lung infection is considered.firstly,the condition that the model has a positive equilibrium point is obtained based on the discriminant of the roots of the cubic polynomial equation,secondly,the specific type of positive equilibrium point of the model and the stability of the positive equilibrium point under the condition are discussed by using the theory of the equilibrium point stability and the theorem of the central manifold,and finally,the emergence of a saddle-node branching at the equilibrium point is considered.

关 键 词：肺部感染模型 稳定性 正平衡点 

分 类 号：O175.26[理学—数学]