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研究生:張登順
研究生(外文):Jhang, Dingshun
論文名稱:藉部分區域穩定理論之 坎-離八卦多重交織導數同步
論文名稱(外文):Kan-Li Hexagram Multiple Symplectic Derivative Synchronization by Partial Region Stability Theory
指導教授:戈正銘戈正銘引用關係
指導教授(外文):Ge, Zhengming
學位類別:碩士
校院名稱:國立交通大學
系所名稱:機械工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:英文
論文頁數:114
中文關鍵詞:chaoschaos synchronization
外文關鍵詞:渾沌系統渾沌同步
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太極為陰陽之結合,而太極渾沌系統即為陽渾沌系統與陰渾沌系統之合併。
陽系統為正數系統,及一般系統,而陰系統則為負數時間之系統。八卦為太極之
延伸,每個卦皆有各自對應的方向、圖形、代表物。八卦同步利用它們各自的圖
形代表三個不同的渾沌系統,接著再用多重交織同步完成八卦同步。六十四卦為
八卦的進階,它分上、下兩部分,這兩部分都代表八卦的一個卦象,而六十四卦
同步即為八卦同步的延伸。同步一般是指系統間存在著主僕般的函數關係。而新
的渾沌多重交織同步則是原來的系統與其他系統間變為伙伴間的函數關係。最後
利用數值模擬來驗證前述計畫。
“Tai Ji”, the great one, is the combination of Yin and Yang, and Tai Ji chaotic system is the combination of “Yang” chaotic system and “Yin” chaotic system. Yang system represents contemporary system, and Yin system means historical system. The eight trigrams, a part of Chinese philosophy, is advance of “Tai Ji”, and they have their own directions, figures, and representations. Trigram synchronization uses three different chaos systems by the figures, and multiple symplectic derivative synchronization is used. Hexagram, advance of the eight trigrams, has two parts, upper and low, which both represent a trigram, and the hexagram synchronization is advance of trigram synchronization. The generalized synchronization is that there exists a functional relationship between the states of the master and those of the slave. A new type of chaotic synchronization, multiple chaotic symplectic 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”. Numerical
simulations are provided to verify the effectiveness of the scheme.
CHINESE ABSTRACT.................................................. iii
ABSTRACT.......................................................... iv
ACKNOWLEDGMENT.................................................... v
CONTENTS ......................................................... vi
Chapter 1 Introduction ........................................... 1
Chapter 2 Chaos of Yang, Yin, and Tai Ji Rossler Systems.......... 4
2-1. Preliminary ................................................. 4
2-2. Yang Rossler system ......................................... 4
2-3. Yin Rossler system .......................................... 5
2-4. Simulation results .......................................... 6
2-5. Tai Ji Rossler system........................................ 12
2-6. Summary ..................................................... 13
Chapter 3 Multiple Symplectic Derivative Synchronization of Ge-Ku-Van der Pol-Rossler System with Other Different Systems by Partial Region
Stability Theory .................................................................. 28
3-1. Preliminary ................................................. 28
3-2. Strategy of multiple symplectic derivative synchronization... 28
3-3. Synchronization by GYC partial region stability theory....... 29
3-4. Synchronization by traditional method........................ 32
3-5. Comparison between new strategy and traditional method....... 33
3-6. Summary...................................................... 35
vii
Chapter 4 Multiple Symplectic Derivative Synchronization of Rossler System and Sprott A System with Variable Time Scales by Partial Region
Stability Theory .................................................................. 47
4-1. Preliminary.................................................. 47
4-2. Synchronization of different time on other octant............ 47
4-3. Synchronization by traditional method........................ 49
4-5. Summary ..................................................... 52
Chapter 5 Kan trigram and Li trigram Multiple Symplectic Derivative
Synchronization by Partial Region Stability Theory .................................................................. 64
5-1. Preliminary.................................................. 64
5-2. Synchronization of Yang and Yin systems...................... 64
5-3. Kan trigram synchronization.................................. 67
5-4. Li trigram synchronization................................... 69
5-5. Summary ..................................................... 72
Chapter 6 Kan-Li Hexagram Multiple Symplectic Derivative Synchronization by Partial Region Stability Theory .................................................................. 88
6-1. Preliminary ................................................. 88
6-2. Systems of Kan-Li hexagram synchronization................... 88
6-3. Kan-Li hexagram synchronization by GYC partial region stability theory ........................................................... 91
6-4. Kan-Li hexagram synchronization by traditional Lyapunov function .................................................................. 93
6-5. Kan-Li hexagram synchronization by linear feedback method .................................................................. 95
6-6. Comparison of synchronization ways........................... 97
6-7. Summary...................................................... 100
Chapter 7 Conclusions .................................................................. 109
References .................................................................. 111
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