湖北民族大学学报（自然科学版）2026，Vol.44Issue(1)：92-100,9.DOI:10.13501/j.cnki.42-1908/n.2026.03.007
具有兴奋效应的肿瘤-免疫模型动力学与倍周期分岔
Dynamics and Period-doubling Bifurcation of Tumor-immune Model with Hormetic Effect
摘要
Abstract
To investigate the effects of hormetic effect and dynamic radiotherapy on tumor cell dynamics,a tumor-immune model with hormetic effect was proposed,and a dynamic regulatory factor was introduced for study.The existence and stability of the fixed points of the model were analyzed.The conditions for period-doubling bifurcation were derived using the center manifold theorem and verified through numerical simulations.The results indicated that the hormetic effect during radiotherapy significantly influenced the number of tumor cells,and that the implementation of dynamic radiotherapy eventually stabilized the tumor cell population near the threshold level.This study provided a theoretical reference for the design of radiotherapy strategies that consider both hormetic effect and dynamic radiotherapy.关键词
肿瘤-免疫模型/稳定性/倍周期分岔/数值模拟/兴奋效应Key words
tumor-immune model/stability/period-doubling bifurcation/numerical simulation/hormetic effect分类
数理科学引用本文复制引用
王佳奇,向长城..具有兴奋效应的肿瘤-免疫模型动力学与倍周期分岔[J].湖北民族大学学报（自然科学版）,2026,44(1):92-100,9.基金项目
国家自然科学基金项目(12361100). （12361100）
