一类随机血糖-胰岛素调节系统的渐近性分析

Analysis of the Asymptotic Properties of a Stochastic Glucose-insulin Regulation System

  • 摘要: 以最基本的IVGTT确定性模型为基础,构建了一个具有白噪声干扰的随机血糖-胰岛素系统.证明了系统正解的存在唯一性,讨论了系统正解的渐近行为.由于随机血糖-胰岛素系统加入了随机项后,其对应的确定性系统的正平衡点将不复存在,为了讨论系统的稳定性,证明了在一定条件下,随机系统的解将围绕确定性系统的正平衡点附近某点做随机振动,且其振动幅度与白噪声干扰强度大小有关.通过数值模拟,探讨了白噪声干扰对系统的影响.

     

    Abstract: A stochastic glucose-insulin regulation system with the perturbation of white noise is investigated. The existence and uniqueness of the positive solution of the system is proved. The asymptotic properties of the positive solution are investigated. There is not a positive equilibrium point for the stochastic system after adding stochastic perturbations to the associated deterministic system. In order to discuss the stability of the system, it is proved that under certain conditions, the solution of the stochastic system will vibrate randomly around the positive equilibrium point of the deterministic system, respectively, and the intensity of this vibration depends on the intensity of the white noise. In addition, the influence of the white noise on system stability is discussed by numerical simulation.

     

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