Yang and Yin parameters in the Lorenz system

Abstract

The history of the Lorenz system is firstly discussed in this paper. In Chinese philosophy, Yin is the negative, historical, or feminine principle in nature, while Yang is the positive, contemporary, or masculine principle in nature. Yin and Yan are two fundamental opposites in Chinese philosophy (therefore, in this paper, these words "Yin parameter," "Yang parameter," "historical system," and "contemporary system" are used to represent the "positive parameter," "negative parameter," "time reversed (-t) system," and "time forward (t) system," respectively). Simulation results show that chaos of historical Lorenz system can be generated when using "Yin" parameters. To our best knowledge, most characters of contemporary Lorenz system are studied in detail, but there are no articles in making a thorough inquiry about the history of Lorenz system. As a result, the chaos of historical Lorenz system with "Yin parameters" is introduced in this paper and various kinds of phenomena in the historical Lorenz system are investigated by Lyapunov exponents, phase portraits, and bifurcation diagrams.