Analysis of Dynamic Five-Element Model

As the theoretical basis of traditional Chinese medicine (TCM), five-element (Wu-Xing) model can generate abundant dynamic phenomena when it is considered as a dynamic system. In this paper, we extent the previous studied model and comprehensively consider all kinds of influence between elements, including "gain", "saturation", "generating", "is-generated", "restricting" and "is-restricted". Based on numerical and analytical cases study, we find that the system will converge to a fixed point or periodic solution, or become chaotic eventually under different settings. The stability is studied by using the first Lyapunov's method and the Lyapunov exponents, and it shows that all these cases are not stable. Additionally, by calculating the rate of change of the volume in phase space, we can judge this model is dissipative for "R&isR" model, but the model with "generation" involved can be dissipative under specific settings.