本論文旨在研究非線性動力學系統，與外加週期驅策訊號之間的混沌相位同步現象。利用週期訊號去驅策雙渦漩吸引子的蔡氏電路與四渦漩吸引子電路之非線性電子電路系統，探究其系統輸出與驅策訊號之間的相位同步。另外，也探究週期激發調制在微晶片型Nd:YVO4雷射及光回饋微晶片型Nd:YVO4雷射的混沌相位同步。
透過頻閃觀測法和遞迴機率分析，呈現這些外加週期驅策非線性動力學系統的相位同步轉換過程；再利用遞迴機率和遞迴機率相關性分析法，去定量驅策訊號與系統輸出之間的相位同步強度。進一步探究在不同驅策振幅與驅策頻率下的相位同步強度。而在相位同步強度關係圖中，可以觀察到象徵同步區間的阿諾德舌頭，數值模擬分析亦呈現與實驗相匹配的結果。

We study the chaotic phase synchronization (CPS) between the external periodically driving signals and the nonlinear dynamic systems. The periodical signal was applied to drive the Chua circuit system with two-scroll attractor and the four-scroll attractor circuit system. The phase synchronization between the outputs of these two circuit systems and the driving signals were investigated. Besides, the chaotic phase synchronization of the periodically pump-modulated microchip Nd:YVO4 laser and the microchip Nd:YVO4 laser with optical feedback were also examined in this study.
Phase synchronization (PS) transition of these periodically driven nonlinear dynamic systems exhibited via the stroboscopic technique and recurrence probability. The recurrence probability and correlation probability of recurrence were utilized to estimate the degree of PS. In this thesis, the degree of PS was studied by taking into account the amplitude and frequency of the external driving signal. The experimental compatible numerical simulations also reflected the fact that the Arnold tongues are experimentally and numerically exhibited in the periodically driven nonlinear dynamic systems.

誌謝........................................................................ i
中文摘要……………………………………………… ii
英文摘要……………………………………………… iii
目錄…………………………………………………… iv
圖次…………………………………………………… vi
第一章 相位同步介紹…………………………….1
1.1 簡介………………………………………1
1.2 相位的定義 ………………………………2
1.3 遞迴機率相位…………………………….5
第二章 週期驅策雙吸引子態蔡氏電路系統之相位同步..9
2.1 非線性電子電路之相位同步簡介………….9
2.2 蔡氏電路系統之實驗架設…………………11
2.3 實驗結果與遞迴量化分析…………………13
2.4 數值模擬結果………………………………22
2.5 小結…………………………………………25
第三章 四渦漩混沌吸引子電路系統之相位同步…26
3.1 四渦漩混沌吸引子系統介紹……………....26
3.2 電路實驗架設………………………………27
3.3 實驗結果與遞迴量化分析…………………31
3.4 數值模擬結果………………………………35
3.5 小結…………………………………………39
第四章 激發調制混沌態之微晶片型Nd:YVO4雷射之相位同步……………….41
4.1 簡介…………………………………………41
4.2 激發調制混沌之單模微晶片型Nd:YVO4雷射..42
4.2.1 實驗量測數據之相位同步分析……………46
4.2.2 數值模擬系統之相位同步分析……….……51
4.3 激發調制混沌之多模微晶片型Nd:YVO4雷射..53
4.3.1 實驗量測數據之相位同步分析……………56
4.3.2 數值模擬系統之相位同步分析……………61
4.4 小結…………………………………………63
第五章 激發調制光回饋微晶片型Nd:YVO4雷射系統之相位同步…………64
5.1 簡介………………………………………64
5.2 實驗系統架設與量測……………………65
5.3 實驗結果與遞迴量化分析………………67
5.4 小結………………………………………72
第六章 結論………………………………………74
參考文獻………………………………………………76
簡歷……………………………………………………78

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