Mathematical modeling of Chinese medicine by complex-valued five-agent network

Traditional Chinese medicine (TCM) is a holistic medicine that deals with the whole person, not just the disease or injury. Based on the Yin-Yang Philosophy and the Wuxing (Five Elements) network, TCM advocates that the human body has the self-regulation ability, which can make the internal organs of the human body operate in a coordinated manner, adapt to changes in the external environment, and achieve harmony between the human body and nature. However, for more than two thousand years, this argument about the human body's self-regulation and adaptation abilities has remained at the level of natural philosophy, lacking direct scientific evidence. This article applies the complex-valued multi-agent network theory to build a general mathematical model for the Yin-Yang Wuxing network based on which, we can quantitatively describe and compute the operation of TCM by linear algebra. The eigenstructure analysis of the established mathematical model clearly reveals the roles of the Yin-Yang philosophy and the Wuxing network in TCM and confirms their inherent feedback mechanism to ensure the balanced operation of organs in the human body. This paper opens the way for quantitative research on TCM, which can be used to identify unbalanced organs and predict the impact of environmental changes and medical treatments on the human body.