臺灣博碩士論文加值系統

本篇論文首先探討動載懸掛系統之渾沌同步現象及同步時的暫態反應。當討論系統的同步現象時，利用李亞普諾夫指數來判斷系統發生同步時的臨界值。可以發現在大部份的同步現象均可以利用此方法來判斷，但在某些的條件之下其還是存在一個誤差。其次將探討自治與非自治系統的同步現象，可很容易發現兩系統不能完全同步，所以將探討它們之間的相位同步現象。又討論渾沌同步在實際秘密通訊上的應用。
最後將探討幾個反控制渾沌的方法，如外加定力矩、外加週期力矩、外加週期脈衝、延遲迴授控制、適應控制。這些反控制的方法可以使系統的週期行為反控制為渾沌現象。

In this thesis, we first study the chaotic synchronization phenomena of the suspended track with moving load system, and the transient response of chaos synchronization. The Lyapunov exponent is utilized to prove the chaos synchronization but under certain conditions it is more complicated. Next, we study the synchronization of autonomous and nonautonomous system. We find that slave systems can not be synchronized with mater system no matter how large is . Next, the phase synchronization between them will be studied. An application of chaos synchronization, secure communication, is presented.
Finally, in order to increase the chaos phenomena, we use anticontrol. Constant torque, periodic torque, periodic impulse signal, time delay function, the adaptive control are used successfully to control the state from order to chaos.

Chinese Abstract…………………………………………… i
Abstract……………………………………………………… ii
Contents……………………………………………………… iii
List of Figures…………………………………………… v
Chapter 1 Introduction……………………………………… 1
Chapter 2 Synchronization Phenomena of Coupled Chaotic Systems…………… 3
2.1 Description of the System Model and Differential Equations of Motion…........ 3
2.2 Synchronization of Unidirectional Coupled Chaotic Systems……………… 6
2.2.1 Synchronization by linear coupled term ………… 7
2.2.2 Synchronization by nonlinear coupling term…… 8
2.3 Synchronization of Mutual Coupled Chaotic Systems……………………… 10
2.3.1 Synchronization by linear coupling term………………………………… 10
2.3.2 Synchronization by nonlinear coupled term……………………………… 11
2.4 Synchronization via Adaptive Feedback……………………………………… 12
2.5 Transient Time for Unidirectional Chaotic Synchronization…………………. 13
2.5.1 Transient time of unidirectional linear coupled system………………….. 13
2.5.2 Transient time of unidirectional nonlinear coupled system……………… 14
2.6 Synchronization of Coupled Chaotic Different Systems……………………... 15
2.7 Application of Synchronization……………………………………………… 17
Chapter 3 Chaos AntiControl
3.1 Chaos Anticontrol by the Addition of Constant Term……………………… 19
3.2 Chaos Anticontrol by the Addition of Periodic Term……………………… 20
3.3 Chaos Anticontrols by the Addition of Periodic Impulse Input……………… 20
3.4 Chaos Anticontrols by the Addition of Delay Feedback Term………… 21
3.5 Chaos Anticontrol by Adaptive Control ……………………………………… 21
3.6 Chaos Anticontrol by The Another Style of Adaptive Control……………… 22
Chapter 4 Conclusions……………………………………… 24
References………………………………………………………… 26

1. Ge Zheng-Ming and Fang Chien-Chih, “Dynamic Analysis and Control of Chaos for a Suspended Track with Moving Load”, accepped by Transactions of Canadian Society for Mechanical Engineering, 2001.
2. Kapitaniak T., Controlling Chaos, Academic Press. London. 1996
3. Eth. Mosekilde, Complexity, Chaos and Biological Evolution, Nato series, Plenum, New York, 1991.
4. S. H. Strogatz, Nonlinear Dynamics and Chaos, Addison, Reading, 1994.
5. Terry John. J. and Vanwiggeren Gregory D.,” Chaotic Communication Using Generalized Synchronization”, Chaos Solitons and Fractals, 2001.
6. Fang Jin-Qing, Hong Yiguang, and Chen Guanrong, “Switching Manifold Approach to Chaos Synchronization”, Physical Review E, Vol. 59, No.3, 1999.
7. Vadivasova T. E., Balanov A. G.., Sosnovtseva O. V., Postnov D. E., and Mosekilde E.,”Synchronization in Driven Chaotic Systems: Diagnostics and Bifurcations”, Physics Letters A 253 66-77, 1999.
8. Paul R.S., Rajaseka S. r 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.
9. Santobont Giovanni, Bishop Steven R. and Varone Alberto, ”Transient Time in Unidirectional Synchronization”, International Journal of Bifurcation and Chaos, Vol. 9, No. 12, 1999.
10. Shuai Jian-Wei and Durand Dominique M., “Phase Synchronization in Two Coupled Chaotic Neurons”, Physics Letters A. 264,289-297, 1999.
11. Parmananda P.,”Generallized Synchronization of Spatiotemporal Chemical Chaos”, Physical Review E, Vol. 56, No.2, 1997.
12. He Rong. and Vaidya P. G.,”Time Delayed Chaotic Systems and Their Synchronization”, Physical Review E, Vol. 59,No. 4, 1998.
13. Junge Lutz and Parlitz Ulrich, “Synchronization Using Dynamic Coupling”,
Physical Review E. Vol. 64, 1997.
14. Jiang Zhong-Ping, “A Note on Chaotic Secure Communication System”, IEEE
Transactions on Circuits and Systems. Vol. 49, No.1, 2002.
15. Liu Yun and Davis Peter, ”Dual Synchronization of Chaos”, Physical Review E,
Vol 61, No3, 2000.
16. Zhan Meng, Zheng Zhi-Gang, Hu Gang, and Peng Xi-Hong, “Nonlocal Chaotic
Phase Synchronization”, Physical Review E, Vol 62, No 3, 2000.
17. Sinha, S., Ramaswamy R. and Rao J. S., “Adaptive Control in Nonlinear
Dynamics”, Physica D, Vol. 43, pp.118-128, 1991.