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

摘要

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.