本論文以希伯特-黃轉換(Hilbert-Huang transform, HHT)分析非線性動力學，主要研究羅侖茲訊號與泵源調製雷射模型兩個系統。由HHT分析羅侖茲(Lorenz)訊號，可發現本質模態函數(Intrinsic Mode Function)平均頻率依序可得到基頻、二分之一基頻、四分之一基頻的結果。在泵源雷射調製系統中的結果為基頻、五分之一基頻、十分之一基頻等，顯示不同的動態系統有不同的基頻變化，但都由簡單分數的基頻組成。除此之外，本質模態函數的平均瞬時頻率對調製深度的變化趨勢與Lyapunov分析結果相互對應，故HHT可作為判斷混沌訊號閥值的參考工具。

In this thesis, we study the nonlinear dynamics by the Hilbert-Huang Transform (HHT).The main researches including the Lorenz attractor and the laser system with pump modulation. Analyzing the Lorenz system by HHT, the result reveals a regular ratio distribution for the fundamental frequency of 1/2, 1/4, and so on. Using HHT to investigate the pump modulated laser output; the ratio relationship of frequency is 1/5, 1/10, 1/20, etc. It shows that the difference of ratio will appear in separate system. Furthermore, HHT can become a tool to distinguish the threshold of chaotic signal due to the trend of frequency in each intrinsic mode function is similar with the Lyapunov exponent analysis.

1.N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung and H. H. Liu, “The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-stationary Time Series Analysis,” Proc. R. Soc. Lond. A, 454, 903–995, (1998).
2.N. E. Huang, S. S. P. Shen, Hilbert-Huang Transform and Its Applications, World Science, Singapore, (2005).
3.Z. Wu, N. E. Huang, J. M. Wallace, B. V. Smoliak, X. Chen, “On the Time-varying Trend in Global-mean Surface Temperature,” Climate Dynamics, 37, 759–773, (2011).
4.Z. X. Liu, H. J. Wang, and S. L. Peng, “Texture Classification Through Directional Empirical Mode Decomposition,” Int. Conf. Pattern Recognition, 4, 803–806, (2004).
5.G. Rilling, P. Flandrin, and P. Goncalves, “Detrending and Denosing with Empirical Mode Decompositions,” 12th EUSIPCO, 1581–1584, Wien, Austria, (2004).
6.Y. H. Shiau, and M. C. Wu, “Detecting Characteristics of Information Masked by a Laser-triggered Microwave System via Hilbert–Huang Transform,” Opt. Commu., 283, 1909–1916, (2010).
7.T. Yalcinkaya, and Y. C. Lai, “Phase Characterization of Chaos,” Phys. rev. lett., 79, 3885–3888, (1997).
8.Y. C. Lai, and N. Ye, “Recent Developments in Chaotic Time Series Analysis,” Int. J. Bifurcation Chaos, 13, 1383–1422, (2003).
9.E. N. Lorenz, J. Atmos. Sci., “Deterministic Nonperiodic Flow,” J. Atmos. Sci., 20, 130–141, (1963).
10.S. Kizhner, K. Blank, T. Flatley, N. E. Huang, D. Petrick, and P. Hestnes, “On Certain Theoretical Developments Underlying the Hilbert-Huang Transform,” IEEEAC, USA, (2006).
11.A. G. Fox and T. Li, “Resonant Modes in a Maser Interferometer,” Bell Syst. Tech. J., 40, 453–488, (1961).
12.Y. J. Cheng, P. L. Mussche, and A. E. Siegman, “Cavity Decay Rate and Relaxation Oscillation Frequency in Unconventional Laser Cavities,” IEEE J. Quantum Electro., 31, 391–398, (1995)
13.M. D. Wei, C. H. Chen, H. H. Wu, D. Y. Huang, and C. H. Chen, “Chaos Suppression in the Transverse Mode Degeneracy Regime of a Pump-modulated Nd:YVO4 Laser,” J. Opt. A: Pure Appl. Opt., 11, 045504, (2009).
14.C.H. Chen, P. T. Tai, M. D. Wei, and W. F. Hsieh, “Multibeam-waist Modes in an End-pumped Nd:YVO4 Laser,” J. Opt. Soc. Am. B, 20, 1220–1226, (2003).