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| 研究生： |
陳健億 Chien-I Chen |
|---|---|
| 論文名稱： |
小波轉換理論利用中位數的方法使用在具備Neumann邊界條件的耦合混沌系統及其同步化應用 Median Approach to the Wavelet Transform Method for the Coupled Chaotic System with Neumann Boundary Conditions and its Synchronous Applications |
| 指導教授： |
李金龍
Chin-Lung Li |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
南大校區系所調整院務中心 - 應用數學系所 應用數學系所(English) |
| 論文出版年： | 2010 |
| 畢業學年度： | 98 |
| 語文別： | 英文 |
| 論文頁數： | 22 |
| 中文關鍵詞： | 小波轉換理論 、Neumann邊界條件 、耦合混沌系統 、同步化應用 |
| 外文關鍵詞： | Wavelet Transform Method, Neumann Boundary Conditions, Coupled Chaotic System, Synchronous Applications |
| 相關次數： | 點閱：2 下載：0 |
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基於master stability function (MSF) [7] 下的耦合混沌系統同步化，混沌同步化的穩定實際上是受到耦合混沌系統內耦合矩陣的第二大固有值所影響。另外小波轉換理論在Wei et al.[11]論證下，可大幅度的增加耦合混沌系統同步化下的耦合能量的應用範圍。在這篇研究中，第一，利用中位數之小波轉換去改進最佳的小波參數之概念被提出，其次，我們在單獨混沌系統具備散佈耦合地Neumann邊界條件下給予一個應用。
Based on the master stability function (MSF) [7] for local synchronization in coupled chaotic systems, the stability of chaotic synchronization is actually controlled by the second largest eigenvalue of the coupling matrix of coupled chaotic systems. In addition, it is demonstrated that the wavelet transform method, which is proposed by Wei et al.[11], can greatly increase the applicable ranges of coupling strengths for local synchronization of coupled chaotic systems. In this research, there are two-fold. First, the concept of the wavelet transform method by using median to improve the best choice of wavelet parameters is proposed. Second, we give an application to the individual chaotic system di usively coupled with Neumann boundary conditions.
[1] Ashwin, P., "Synchronization from chaos," Nature (London) 422, 384-385 (2003).
[2] Daubechies, I., Ten Lectures on Wavelets, CBMS-NSF Series in Applied Mathematics(SIAM, Philadelphia, 1992).
[3] Davis, P. J., Circulant Matrices (Wiley, New York,1979).
[4] Guan, S., Lai C. H., and Wei, G. W., "A wavelet method for the characterization of spatiotemporal patterns," Physica D 163, 49-79 (2002).
[5] Motter, A. E., Zhou, C. S., and Kurths, J., "Enhancing complex-network synchronization," Europhys. Lett. 69, 334-340 (2005).
[6] Ott, E., Grebogi, C., and York, J. A., "Controlling chaos," Phys. Rev. Lett. 64, 1196-1199 (1999).
[7] Pecora, L. M. and Carroll T. L., "Master stability functions for synchronized coupled systems," Phys. Rev. Lett. 80, 2109-2122 (1998).
[8] Pecora, L. M. and Carroll, T. L., "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990).
[9] Shieh, S. F., Wei, G. W., Wang, Y. Q., and Lai, C.-H., "Mathematical proof for wavelet method of chaos control," J. Math. Phys. (to be published).
[10] Wei, G. W., "Synchronization of single-side locally averaged adaptive coupling and its application to shock capturing," Phys. Rev. Lett. 86, 3542-3545 (2001).
[11] Wei, G. W., Zhan, M., and Lai, C.-H., "Tailoring wavelets for chaos control," Phys. Rev. Lett. 89, 284103 (2002).
[12] Wu. C. W., Perturbation of coupling matrices and its effect on the synchronizability in arrays of coupled chaotic systems," Phys. Lett. A 319, 495-503 (2003).
[13] Yang, J., Hu, G., and Xiao, J., "Chaos synchronization in coupled chaotic oscillators with multiple positive Lyapunov exponents," Phys. Rev. Lett. 80, 496-499 (1998).
[14] Zhan, M., Wang, X. G., and Gong, X. F., "Complete synchronization and generalized synchronization of one-way coupled time-delay systems," Phys. Rev. E 68(3), 036208 (2003).
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