Mathematical analysis of Yin-Yang Wu-Xing Model in TCM

摘要

以五行系统为研究对象, 在深入认识五行系统运动关系的基础上, 设定动力学 模型的四个基本假设; 设定动力学模型的模型期望, 即以人体五脏对应五行, 以五脏为 核心的人体自调节系统的运动对应五行动力学模型中五行的运动, 以人体健康、亚健康或病理状态平台期、 健康恶化三种状态对应五行数学模型中的平衡态、 暂时平衡(或准动态平衡)、 失稳三种状态; 根据五行生克乘侮关系设定模型参数, 建立了五行系统动力学模型, 该动力学模型在数学上是一个五元一次常微分方程组。 通过对该模型的冲击 响应研究结果表明, 冲击型激励能够降低系统的“回归阈值”, 提高系统的健康程度。 存在三种方式来降低“回归阈值”, 与五行系统运行法则和中医临床实践的经验规律相符合。

Abstract

According to Traditional Chinese Medicine, the functional structure of human body is composed of five functional subsystems which are based on the five-organs concept, and the relationship between them could be expatiated with Wu-Xing (Five-Elements) theory. Wu-Xing system is taken as our research object. The dynamic model has the characteristic of self-organization. There is only one stable point with local stability in the five-dimensional space. There exists an instability domain in the five-dimensional space. The stability domain is unbounded; it contains some special subdomains, including rectilineal subdomains, ray subdomains and line subdomains. In some ray subdomains, there exists “comeback summits”, the peak value of the comeback summit is comeback threshold. The existence of the comeback threshold means that, if the human body wants to go back to the healthy state from a certain special state which corresponded to the initial conditions located in a domain with comeback summit, it has to get across the comeback threshold. The comeback threshold is the division of the healthy state and the sub-healthy state. Some research work is done to investigate the response of the Wu-Xing dynamic model to the impact stimulation, and results in the decrease of the system’s comeback threshold. There are 3 manners to achieve this goal, and they tally with the principle of the Wu-Xing system and the experimental rules in clinic.