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研究生:黃裕峰
研究生(外文):Yuh-Fung Huang
論文名稱:調制在非線性系統的動力學效應之研究
論文名稱(外文):The Study on the Modulation Responses of Nonlinear Dynamical Systems
指導教授:翁恒義陳志隆陳志隆引用關係
指導教授(外文):Herng-Yih UengJyh-Long Chern
學位類別:博士
校院名稱:國立中山大學
系所名稱:電機工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:1999
畢業學年度:87
語文別:英文
論文頁數:79
中文關鍵詞:調制非線性動力學
外文關鍵詞:modulationnonlineardynamical
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在本論文中研究調制在非線性系統的動力學效應,其中包含三種不同被調制系統:利用調制的綠光雷射照在由氖燈所構成的光阻抗(optogalvanic) 系統,利用調制的周期訊號去驅動一個非線性二極體的共振子系統,以及一個被調制的半導體雷射系統。
首先,利用調制的綠光雷射照在由氖燈所構成的光阻抗系統中,觀察到周期相加現象,周期相加是一個很奇妙的惡魔階梯結構,與其他分歧結構(bifurcation structure)相比,如周期倍增(period-doubleing)或間歇性(intermittency),它是較少被觀察到。這裡提供一個非常有趣的非線性系統在其中周期相加是固有的。
更進一步的利用這個惡魔階梯結構的鎖頻系統,在兩個鎖頻狀態中,其中間隱含有無窮多周期態,其周期性能以Farey tree 結構說明。因為在兩個鎖頻狀態中的範圍通常是很小,如此一碎形(fractal)結構可被用來當作某一特定周期態的訊號產生源,並且不會改變到系統參數。另一方面,由於外在擾動的非線性反應,一碎形結構可被用來當作一偵測器,可被調到大多數的弱周期訊號。這兩個有潛力應用被研究且已在此一氖燈所構成的光阻抗系統中被驗證。
其次,利用調制的周期訊號與雜訊訊號混合去驅動一個非線性二極體的共振子系統,去觀察其動力學。很多反直覺特徵,例如雜訊誘導秩序產生和雜訊壓制混沌訊號,在此實驗系統中被驗證。這些特徵被獨特誘導以多重性(multiplicative)動力學雜訊取代純加法性(additive)動力學雜訊,雜訊誘導秩序、多重性動力學雜訊和相干共振(coherence resonance)中之奇妙關連亦被在此證明。
最後,從一被調制的半導體雷射系統,利用奇異值分解特徵值(singular value decomposition)頻譜方法去探討複雜時間序列中的決定論特性。利用此一方法,混沌訊號的特性能很快被驗證,雜訊之含量比例亦能很快被估計,加在半導體雷射的調制量與雜訊量之關聯亦可被說明,相對雜訊強度(relative intensity noise)和奇異值分解特徵值頻譜的雜訊層(noise floor) 中之關連亦被在此清楚證明。
In this thesis, the studies of the modulation responses of three major nonlinear dynamical systems have been presented. The studies were separated into three parts, an optogalvanic system consisting of a neon bulb shone by a modulated green-light He-Ne laser, a periodically-driven nonlinear diode resonator system, and a modulated semiconductor laser system.
In the first part, I show an optogalvanic system consisting of a neon bulb shone by a modulated green-light He-Ne laser exhibits period-adding. Period-adding is a novel devil''s staircase structure that, however, is less observed in comparison with the other bifurcation structures, such as period-doubling and intermittency. This suggests an interesting class of nonlinear systems where period-adding is inherent.
The further employment of this frequency locking system with the devil''s staircase structure that is between the two frequency locking states there embeds an almost infinite number of states whose periodicities could be specified by the Farey tree was also presented. Since the range between two specific states is usually small, such a fractal system may be utilized as a generating source of signals with specific periodicity without greatly modifying the system''s parameters. On the other hand, due to its nonlinear response to external perturbations, a fractal system may be tuned to act as a detector for a variety of weak periodic signals. These two potential applications are investigated and experimentally demonstrated in this He-Ne laser optogalvanic system.
The second part contains the noise-associated dynamical behavior of a periodically-driven nonlinear diode resonator system. Several counter-intuitive features, such as noise- induced order and stochastic suppression of chaos, are experimentally identified. These features are uniquely induced by the multiplicative dynamical noise rather than by the additive dynamical noise. The novel connections between multiplicative dynamical noise, noise-induced linearisation and coherence resonance are shown.
At the last part, a singular value decomposition (SVD) eigenvalue spectrum has been employed to explore the deterministic nature of the complex time series from a modulated semiconductor laser. With this method, the signature of chaos can be quickly identified and the noise contamination ratio can also be estimated. Relations between the supplied modulation of laser diode and the noise level are illustrated. The connection between relative intensity noise (RIN) and the noise floor in the SVD spectrum has also been clarified.
Cover
Abstract in Chinese
Abstract in English
Table of Contents
List of Figures
List of Tables
Chapter One Introduction
1.1 dynamical systems
1.2 Fractals
1.3 Strange attractor
1.4 An overview of the dissertation
Chapter Two Observation of period-adding in an optogalvanic circuit
2.1 Introduction
2.2 Experimental setup and its characterization
2.3 Experimental results
2.4 Discussions and conclusions
Chapter Three Nonlinear Response of Optogalvanic Fractal and Its Application to Signal Processing
3.1 Introduction
3.2 Experimental Setup
3.3 Experimental Results-Perturbation of Elctrical Signal
3.4 Experimental Results-Perturbation of Optical Signal
3.5 Connection to Mapping Dynamics
3.6 Conclusions and Discussions
Chapter Four Noise-induced Linearusation and Coherene Enhancement:Experimental Evidence
4.1 Introduction
4.2 Experimental Setup
4.3 Experimental results
4.4 Discussions and conclusions
Chapter Five Complex Time Series from a Modelated Semiconductor Laser:Its Determinism Exporation
5.1 Introduction
5.2 SVD characterization scheme
5.3 Experimental Apparatus
5.4 Laser Diode Studies
5.5 Connection to Relative Intensity Noise(RIN)
5.6 Conclusions
Chapter Six Concluding Remarks
Reference
Publication list
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