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研究生:游佳洋
研究生(外文):Chia-Yang Yu
論文名稱:旋轉支點單擺之渾沌同步與反控制
論文名稱(外文):Chaos Synchronization and Chaos Anticontrol of a Rotationally Supported Simple Pendulum
指導教授:戈正銘戈正銘引用關係
指導教授(外文):Zheng-Ming Ge
學位類別:碩士
校院名稱:國立交通大學
系所名稱:機械工程系
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:2002
畢業學年度:90
語文別:中文
論文頁數:86
中文關鍵詞:渾沌同步反控制
外文關鍵詞:ChaosSynchronizationAnticontrol
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本篇論文主要探討旋轉支點單擺系統之渾沌同步與反控制。首先運用外加不同的耦合項與observed-based的方法,使得兩個不同初始值的渾沌系統達到同步,並藉由相平面圖、李亞普諾夫指數、龐加萊映射法、同步時間來做驗證。再利用歐幾里得幾何距離畫出同步系統單向耦合強度與距離的關係圖,並分析初始值與耦合強度對系統暫態的行為的影響。接著在渾沌同步應用方面,利用渾沌系統的狀態變數作為加碼與解碼函數變數,並模擬完成整個秘密通訊系統。在渾沌反控制部分,以外加控制項包括常數項、週期函數、週期脈衝、時間延遲以及適應控制,使原本為週期行為的系統控制到渾沌行為、並由李亞普諾夫指數以及分叉圖來驗證其控制結果。

Chaos synchronization and anticontrol of a rotationally supported simple pendulum studied in this thesis. Different kinds of coupling terms are used to synchronize the two identical chaotic systems with different initial conditions. An observed-based scheme is also used to achieve synchronization. The results are demonstrated by phase portrait, Lyapunov exponent, Poincaré maps and synchronization time. Next, in order to analyze the transient behavior of the synchronized systems, Euclidean distance is used to plot a figure with coupling strength versus the distance. The chaotic signals are used to mask the message function in the secure communication system. Finally, anticontrol of chaos is achieved by adding constant term, periodic term, impulse term, time-delay term and adaptive control.

CHINESE ABSTRACT ………………………………………………………………..i
ENGLISH ABSTRACT ……………………………………………………………….ii
CONTENTS …………………………………………… …..iii
LIST OF TABLES AND FIGURES ……………………………………………………………….iv
Chapter 1 Introduction ……………………………………………………………….1
Chapter 2 Chaos Synchronization for The Coupled System ………………………………………………………….…..3
2.1 Description of the System Model and Differential
Equations of Motion ………………………………………………………….....3
2.2 Chaos Synchronization of Unidirectional Coupled
Systems ……………………………….…………………..4
2.2.1 Coupling by linear term ……………………………………………...............4
2.2.2 Coupling by periodic term
.................…………………………………………6
2.2.3 Coupling by exponential term …………………………………….....................7
2.3 Chaos Synchronization of Mutual Coupled Systems …………………….................................8
2.3.1 Coupling by linear term ……………………………………………...............8
2.3.2 Coupling by periodic term ………………………………………….................9
2.3.3 Coupling by exponential term ……………………………………....................10
2.4 Observed-based Synchronization Scheme ………………………………........................11
2.5 Transient Time in Unidirectional Synchronization ………………………..............................12
Chapter 3 Chaotic Secure Communication Systems
…………………...………….......................14
Chapter 4 Anticontrol of Chaos ……………………………………………………........17
4.1 Anticontrol of Chaos by Adding Constant Term …………………………............................17
4.2 Anticontrol of Chaos by Adding Periodic Term …………………………............................18
4.3 Anticontrol of Chaos by Adding Periodic Impulse Term ………………....................................18
4.4 Anticontrol of Chaos by Adding Delay Feedback Term …………………..................................19
4.5 Adaptive Control …………………………………………………………....19
Chapter 5 Conclusions ……………………………………………………………..21
References …………………………………………….…22

REFERENCES
[1] Kapitaniak, T., Controlling Chaos, Academic Press. London. 1996.
[2] Mosekilde, E., Complexity, Chaos and Biological Evolution, Nato series, Plenum, New York, 1991.
[3] Strogatz, S. H., Nonlinear Dynamics, and Chaos, Addison, Reading, 1994.
[4] Terry, John J. and VanWiggeren Gregory D., “ Chaotic Communication Using Generalized Synchronization”, Chaos Solitons and Fractals, Vol. 12, pp.145-152, 2001.
[5] Sarasola C., Torrealdea F.J., d’Anjou, A., and Grana M., ” Synchronization of Non-Identical Chaotic Systems”, Control of Oscillations and Chaos, 2000 Proceedings. 2000 2nd International Conference, Vol. 3, pp. 475 -479 Vol. 3, 2000.
[6] Santobont, Giovanni, Bishop Steven R. and Varone, Alberto, “Transient Time in Unidirectional Synchronization”, International Journal of Bifurcation and Chaos, Vol. 9, No. 12, 1999.
[7] Murali, K. and Lakshmanan, M., “ Secure Communication Using a Compound Signal from Generalized Synchronicale chaotic systems”, Physics Letters A, Vol. 241 pp.303-310, 1998.
[8] Vadivasova, T. E., Balanov, A. G., Sosnovtseva O. V., D. E. Postnov and E. Mosekilde, ”Synchronization in Driven Chaotic Systems: Diagnostics and Bifurcations”, Physics Letters A, Vol. 253, pp. 66-77, 1999.
[9] Paul, R. S., Rajasekar, S. and Murali, K., “Coexisting Chaotic Attractors, Their Basin of Attractions and Synchronization of Chaos in Two Coupled Duffing Oscillators”, Physics Letters A, pp283-288, 1999.
[10] Corron, N. J. and Hahs, D. W., “ A New Approach to Communications Using Chaotic Signals”, IEEE Trans. Circuits Syst. I, Vol. 44, pp.373-382, 1997.
[11] Liu Y., Chen H. F., Liu J. M., Davis P. and Aida T., “ Communication Using Synchronization of Optical-Feedback-Induced Chaos in Semiconductor Lasers”, Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on, Vol. 48 Issue: 12, pp.1484 —1490, 2001.
[12] Jiang, Zhong-Ping, “A Note on Chaotic Secure Communication Systems”, Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on, Vol. 49 Issue: 1, pp. 92 —96, 2002.
[13] Chen, Guanrong, “ Control and Anticontrol of Chaos”, Control of Oscillations and Chaos, 1997. Proceedings, 1997 1st International Conference, Vol. 2, pp.181 -186, 1997.
[14] Chen, Guanrong and Lai, Dejian, “ Anticontrol of Chaos via Feedback”, Decision and Control, 1997, Proceedings of the 36th IEEE Conference on, Vol. 1, pp.367 -372, 1997.
[15] Chen, Guanrong and Dong, Xiaoning, From Chaos to Order, World Scientific, New Jersey, pp.177, pp.335, 1998.

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