一类具有β细胞功能的血糖-胰岛素快慢系统研究

Analysis of a Slow-Fast System for Glucose-Insulin Regulatory withβCell Function

提出了一类具有β细胞功能的血糖-胰岛素快慢系统数学模型.首先将β细胞质量当作参数,讨论了快子系统平衡点稳定性,进而研究了全系统的动力学行为,包括系统平衡点的存在性、边界平衡点的稳定性、正平衡点的局部稳定性以及Hopf分支现象等.进一步从生理上讨论了β细胞质量变化对调节系统的影响.

A kind of mathematical model of the glucose-insulin regulatory system with the mass ofβcells as variables is proposed.Firstly,the stability of the positive equilibrium for the fast subsystem is discussed,and then the full system behaviors are studied,including the existence of the system equilibrium,the stability of the boundary equilibrium,the local stability of the positive equilibrium and the Hopf bifurcation phenomenon.The effects ofβcell mass on the regulatory system are further discussed physiologically.