藉部分區域穩定理論之艮-巽八卦多重交織導數同步

Abstract

廣義同步是存在著主僕狀態之間的一個函數關係。一個新型的混沌同步，藉由部分區域穩定理論之多重交織導數同步，得到與原系統狀態變量和其他不同系統構成的“夥伴”關係。利用數值模擬來驗證部分區域穩定理論之多重交織導數同步的有效性。 在中國哲學中，陰代表是負或陰柔，而陽是代表正或陽剛。陰跟陽在中國哲學中兩個是互相對立的，然而太極結合陰陽，這可能意味著宇宙的起源。八卦是中國哲學的一部分，他們擁有各自的方位、數字、以及代表性。最後，結合了在上面的艮卦與在下面巽卦得到六十四卦的艮-巽卦。艮-巽卦代表不同的混沌系統，並藉由部分區域穩定理論達成多重交織導數同步。

Yin and Yang are two fundamental opposites in Chinese philosophy. Chaos of contemporary Chen system, i.e. Yang chaos of Chen system, has been investigated completely. In this proposal, chaos of historical Chen system, i.e. Yin chaos of Chen system, is studied with comparison to that of Yang chaos by time histories of states, phase portraits, bifurcation diagrams and Lyapunov exponents. Furthermore, by Chinese philosophy, Tai Ji chaos, i.e. Great One chaos, which consists of Yin chaos and Yang chaos, of Chen system is studied firstly. The generalized synchronization is that there exists a functional relationship between the states of the master and those of the slave. A new strategy to achieve chaos generalized synchronization and multiple symplectic derivative synchronization, is obtained with the state variables of the original system and of another different order system as constituents of the functional relation of “partners”. Finally, numerical simulations are given to verify the effectiveness of the proposed scheme examples. “The Book of Changes” is a classic text of Chinese culture. In this thesis, the trigram consisted by three broked lines or unbroken lines forms various chaos synchronization. Numerical simulations in examples of Gen and Xun trigram generalized synchronization are given to verify the effectiveness of the proposed scheme. Finally, combining Gen trigram in upper place and Xun trigram in lower place can get Gen-Xun hexagram. Gen-Xun hexagram can be annotated by Chaos and its synchronization.