Research on modern nonlinear dynamic model of five-elements theory.

This article studied on five elements system and set general and strict model expectations combining with Traditional Chinese Medicine Zang-fu organs theory, in which absolute stable state, conditional stable state or transient stability and instability in mathematical models were corresponding to human healthy state, sub-healthy state (pathological plateau phase) and health deterioration state respectively. Model parameters were set up according to the mutual generation and restriction relations among five elements. The dynamic model of Five-Elements System was built, of which impulse responses were corresponding to human response under TCM treatment. Analyses of initial value and excitation response were conducted by numerical simulation and results turned out to meet the requirements of general model expectation: five elements system dynamic model had self-organization function; there existed only one non-global stable point and instability region in the five-dimensional space consisting of variables, in which instability was corresponding to pathological deterioration; system stable region was an unbounded domain and it included the stable sub-regions of special straight line-type, ray-type and line segment-type. Among those ray-types, some contained "Regression Peak" were classed as conditional stable regions while others as absolute ones. The existence of this peak indicates that our body must exceed a "Regression Threshold" when transiting from sub-healthy state (pathological plateau phase) to healthy state through self-regulation mechanism. Impulse excitation can reduce certain threshold and then increase the system health level, which is complied with the operating principle of Five-Elements System and the empirical rule of TCM clinical practice. This model has revealed qualitatively the inherent movement law of Five-Elements System and thus provides a new analysis tool for basic theoretical study on TCM.