应用数学和力学2026，Vol.47Issue(2)：243-256,14.DOI:10.21656/1000-0887.460021
一类糖尿病模型的动力学行为及敏感性分析
Dynamic Behavior and Sensitivity Analysis on a Class of Diabetes Models
摘要
Abstract
Based on the fact that glucocorticoid induces insulin resistance,a new type of diabetes model invol-ving insulin,glucose,and glucocorticoid was established to explore the complex pathogenesis of diabetes.Firstly,the local and global stability of the equilibrium point was demonstrated with the linearization method,the limit system theory,and the Dulac criterion.Secondly,the key parameters affecting glucose concentration were selected,and the sensitivity analysis of the key parameters with respect to the positive equilibrium point was carried out with the direct differentiation method.This analysis shows how the key parameters influence the secretion and function of insulin and glucocorticoid,thereby helping to regulate the fluctuations of glucose levels.Finally,numerical simulations were conducted on MATLAB.These simulations not only verify the cor-rectness of the theoretical analysis,but also reveal the changing trends of glucose concentrations under differ-ent intervention treatments.The results indicate that,the selection of appropriate key parameters is crucial for the control of glucose concentration,which provides a theoretical basis for formulating clinical treatment plans for diabetes.关键词
糖尿病模型/稳定性/Dulac判据/敏感性分析Key words
diabetes model/stability/Dulac criterion/sensitivity analysis分类
数理科学引用本文复制引用
李畅通,田佳,冯孝周,刘云涛..一类糖尿病模型的动力学行为及敏感性分析[J].应用数学和力学,2026,47(2):243-256,14.基金项目
陕西省哲学社会科学研究专项(2025YB0201) （2025YB0201）
陕西省外国专家服务计划项目(2024WZ-YBXM-01) （2024WZ-YBXM-01）
国家自然科学基金(12326417) （12326417）
国家外专项目(G2023041033L) （G2023041033L）
