师向云, 高喜文. 一类具有β细胞功能的血糖-胰岛素快慢系统研究[J]. 信阳师范学院学报(自然科学版), 2020, 33(4): 517-521. DOI: 10.3969/j.issn.1003-0972.2020.04.001
引用本文: 师向云, 高喜文. 一类具有β细胞功能的血糖-胰岛素快慢系统研究[J]. 信阳师范学院学报(自然科学版), 2020, 33(4): 517-521. DOI: 10.3969/j.issn.1003-0972.2020.04.001
SHI Xiangyun, GAO Xiwen. Analysis of a Slow-Fast System for Glucose-Insulin Regulatory with β Cell Function[J]. Journal of Xinyang Normal University (Natural Science Edition), 2020, 33(4): 517-521. DOI: 10.3969/j.issn.1003-0972.2020.04.001
Citation: SHI Xiangyun, GAO Xiwen. Analysis of a Slow-Fast System for Glucose-Insulin Regulatory with β Cell Function[J]. Journal of Xinyang Normal University (Natural Science Edition), 2020, 33(4): 517-521. DOI: 10.3969/j.issn.1003-0972.2020.04.001

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 with β Cell Function

  • 摘要: 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.

     

    Abstract: A kind of mathematical model of the glucose-insulin regulatory system with the mass of β cells 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 of β cell mass on the regulatory system are further discussed physiologically.

     

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