A new study of chaotic behavior and the existence of Feigenbaum's constants in fractional-degree Yin-Yang Henon maps

Abstract

In this paper, we firstly develop fractional-degree H,non maps with increasing and decreasing argument n. Yin and Yang are two fundamental opposites in Chinese philosophy. Yin represents the moon and is the decreasing, negative, historical, or feminine principle in nature, while Yang represents the sun and is the increasing, positive, contemporary, or masculine principle in nature. Chaos produced by increasing n is called Yang chaos, that by decreasing n Yin chaos, respectively. The simulation results show that chaos appears via positive Lyapunov exponents, bifurcation diagrams, and phase portraits. In order to examine the existence of chaotic behaviors in fractional-degree Yin-Yang H,non maps, Feigenbaum's constants are measured in this paper. It is found that the Feigenbaum's constants in fractional-degree Yin-Yang H,non maps are of great precision to the first and second Feigenbaum's constants. A detailed analysis of the chaotic behaviors is also performed for the fractional-degree H,non maps with increasing (Yang) and decreasing (Yin) argument n.